{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import font_manager\n",
    "\n",
    "# 设置中文字体\n",
    "font = font_manager.FontProperties(fname=r'C:\\Windows\\Fonts\\msyh.ttc')  # Windows上字体路径，具体根据系统调整\n",
    "plt.rcParams['font.family'] = font.get_name()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 第五节 含参变量的积分\n",
    "\n",
    "设$f(x,y)$是矩形（闭区域）$R = [a,b] \\times [c,d]$上的连续函数。在$[a,b]$上任意取定$x$的一个值，于是$f(x,y)$是变量$y$在$[c,d]$上的一个一元连续函数，从而积分\n",
    "\n",
    "$$\n",
    "\\int_{c}^{d} f(x,y) \\, dy\n",
    "$$\n",
    "\n",
    "存在，这个积分的值依赖于取定的$x$的值。当$x$的值改变时，一般说来这个积分的值也跟着改变。这个积分确定一个定义在$[a,b]$上的$x$的函数，把它记作$\\varphi(x)$，即\n",
    "\n",
    "$$\n",
    "\\varphi(x) = \\int_{c}^{d} f(x,y) \\, dy \\quad (a \\leq x \\leq b).\n",
    "$$\n",
    "\n",
    "(5 - 1)\n",
    "\n",
    "这里变量$x$在积分过程中是一个常量，通常称它为参变量，因此(5 - 1)式右端是一个含参变量的积分，这个积分确定$x$的一个函数$\\varphi(x)$，下面讨论关于$\\varphi(x)$的一些性质。\n",
    "\n",
    "# 定理1\n",
    "\n",
    "如果函数$f(x,y)$在矩形$R = [a,b] \\times [c,d]$上连续，那么由积分(5 - 1)确定的函数$\\varphi(x)$在$[a,b]$上也连续。\n",
    "\n",
    "**证：**\n",
    "\n",
    "设$x$和$x + \\Delta x$是$[a,b]$上的两点，则\n",
    "\n",
    "$$\n",
    "\\varphi(x + \\Delta x) - \\varphi(x) = \\int_{c}^{d} \\left[ f(x + \\Delta x, y) - f(x, y) \\right] \\, dy.\n",
    "$$\n",
    "\n",
    "由于$f(x,y)$在闭区域$R$上连续，从而一致连续。因此对于任意取定的$\\varepsilon > 0$，存在$\\delta > 0$，使得对于$R$内的任意两点$(x_1, y_1)$及$(x_2, y_2)$，只要它们之间的距离小于$\\delta$，即\n",
    "\n",
    "$$\n",
    "\\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} < \\delta\n",
    "$$\n",
    "\n",
    "就有\n",
    "\n",
    "$$\n",
    "| f(x_2, y_2) - f(x_1, y_1) | < \\varepsilon.\n",
    "$$\n",
    "\n",
    "因为点$(x + \\Delta x, y)$与$(x, y)$的距离等于$|\\Delta x|$，所以当$|\\Delta x| < \\delta$时，就有\n",
    "\n",
    "$$\n",
    "| f(x + \\Delta x, y) - f(x, y) | < \\varepsilon.\n",
    "$$\n",
    "\n",
    "于是由(5 - 2)式有\n",
    "\n",
    "$$\n",
    "|\\varphi(x + \\Delta x) - \\varphi(x)| \\leq \\int_{c}^{d} \\left| f(x + \\Delta x, y) - f(x, y) \\right| \\, dy < \\varepsilon (d - c).\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "最大差异：0.07575757575757791\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import quad\n",
    "\n",
    "# 定义函数 f(x, y)\n",
    "def f(x, y):\n",
    "    # 这里使用一个简单的连续函数，例如 f(x, y) = x * y\n",
    "    return x * y\n",
    "\n",
    "# 定义 φ(x)\n",
    "def phi(x, c, d):\n",
    "    # 计算定积分 φ(x) = ∫[c,d] f(x, y) dy\n",
    "    result, _ = quad(f, c, d, args=(x,))\n",
    "    return result\n",
    "\n",
    "# 定义计算连续性的函数\n",
    "def check_continuity(a, b, c, d, delta_x=1e-2):\n",
    "    x_vals = np.linspace(a, b, 100)\n",
    "    phi_vals = np.array([phi(x, c, d) for x in x_vals])\n",
    "\n",
    "    # 计算相邻点的差异\n",
    "    phi_diff = np.abs(phi_vals[1:] - phi_vals[:-1])\n",
    "    \n",
    "    # 绘制 φ(x) 和相邻差异\n",
    "    plt.figure(figsize=(10, 5))\n",
    "    \n",
    "    plt.subplot(1, 2, 1)\n",
    "    plt.plot(x_vals, phi_vals, label=r'$\\varphi(x)$')\n",
    "    plt.title(r'$\\varphi(x)$ as a function of $x$')\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel(r'$\\varphi(x)$')\n",
    "    plt.grid(True)\n",
    "\n",
    "    plt.subplot(1, 2, 2)\n",
    "    plt.plot(x_vals[:-1], phi_diff, label=r'$|\\varphi(x + \\Delta x) - \\varphi(x)|$')\n",
    "    plt.title(r'Difference between $\\varphi(x)$ and $\\varphi(x + \\Delta x)$')\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel(r'$|\\varphi(x + \\Delta x) - \\varphi(x)|$')\n",
    "    plt.grid(True)\n",
    "\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "\n",
    "    # 返回最大差异\n",
    "    max_diff = np.max(phi_diff)\n",
    "    return max_diff\n",
    "\n",
    "# 设置积分区间 [a, b] 和 [c, d]\n",
    "a, b = 0, 5  # 对 x 的区间 [a, b]\n",
    "c, d = 1, 2  # 对 y 的区间 [c, d]\n",
    "\n",
    "# 检查 φ(x) 的连续性\n",
    "max_diff = check_continuity(a, b, c, d)\n",
    "\n",
    "print(f\"最大差异：{max_diff}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "既然函数$\\varphi$在$[a,b]$上连续，那么它在$[a,b]$上的积分存在，这个积分可以写为：\n",
    "\n",
    "$$\n",
    "\\int_{a}^{b} \\varphi(x) \\, dx = \\int_{a}^{b} \\left[ \\int_{c}^{d} f(x,y) \\, dy \\right] \\, dx = \\int_{c}^{d} \\left[ \\int_{a}^{b} f(x,y) \\, dx \\right] \\, dy.\n",
    "$$\n",
    "\n",
    "右端积分是函数$f(x,y)$先对$y$后对$x$的二次积分。当$f(x,y)$在矩形$R$上连续时，$f(x,y)$在$R$上的二重积分\n",
    "\n",
    "$$\n",
    "\\iint_{R} f(x,y) \\, dx \\, dy\n",
    "$$\n",
    "\n",
    "是存在的，这个二重积分化为二次积分来计算时，如果先对$y$后对$x$积分，就是上面的这个二次积分。但二重积分\n",
    "\n",
    "$$\n",
    "\\iint_{R} f(x,y) \\, dx \\, dy\n",
    "$$\n",
    "\n",
    "也可化为先对$x$后对$y$的二次积分\n",
    "\n",
    "$$\n",
    "\\int_{c}^{d} \\left[ \\int_{a}^{b} f(x,y) \\, dx \\right] \\, dy.\n",
    "$$\n",
    "\n",
    "因此有下面的定理2。\n",
    "\n",
    "## 定理2\n",
    "\n",
    "如果函数$f(x,y)$在矩形$R = [a,b] \\times [c,d]$上连续，那么\n",
    "\n",
    "$$\n",
    "\\int_{a}^{b} \\left[ \\int_{c}^{d} f(x,y) \\, dy \\right] \\, dx = \\int_{c}^{d} \\left[ \\int_{a}^{b} f(x,y) \\, dx \\right] \\, dy. \\quad (5 - 3)\n",
    "$$\n",
    "\n",
    "公式$(5 - 3)$也可写成：\n",
    "\n",
    "$$\n",
    "\\int_{a}^{b} dx \\int_{c}^{d} f(x,y) \\, dy = \\int_{c}^{d} dy \\int_{a}^{b} f(x,y) \\, dx. \\quad (5 - 3')\n",
    "$$\n",
    "\n",
    "下面考虑由积分(5 - 1)确定的函数$\\varphi(x)$的微分问题。\n",
    "\n",
    "# 定理3\n",
    "\n",
    "如果函数$f(x,y)$及其偏导数$f_{x}(x,y)$都在矩形$R = [a,b] \\times [c,d]$上连续，那么由积分(5 - 1)确定的函数$\\varphi(x)$在$[a,b]$上可微，并且\n",
    "\n",
    "$$\n",
    "\\varphi'(x) = \\frac{d}{dx} \\int_{c}^{d} f(x,y) \\, dy = \\int_{c}^{d} f_{x}(x,y) \\, dy. \\quad (5 - 4)\n",
    "$$\n",
    "\n",
    "*证：**\n",
    "\n",
    "因为\n",
    "\n",
    "$$\n",
    "\\varphi'(x) = \\lim_{\\Delta x \\to 0} \\frac{\\varphi(x + \\Delta x) - \\varphi(x)}{\\Delta x},\n",
    "$$\n",
    "\n",
    "为了求$\\varphi'(x)$，先利用公式(5 - 2)作出增量之比\n",
    "\n",
    "$$\n",
    "\\frac{\\varphi(x + \\Delta x) - \\varphi(x)}{\\Delta x} = \\frac{1}{\\Delta x} \\int_{c}^{d} \\left[ f(x + \\Delta x, y) - f(x, y) \\right] \\, dy. \\quad (5 - 5)\n",
    "$$\n",
    "\n",
    "由拉格朗日中值定理以及$f_{x}(x,y)$的一致连续性，可得\n",
    "\n",
    "$$\n",
    "f(x + \\Delta x, y) - f(x, y) = f_{x}(x + \\theta \\Delta x, y) \\Delta x = f_{x}(x, y) + \\eta(x, y, \\Delta x),\n",
    "$$\n",
    "\n",
    "其中$0 < \\theta < 1$，$|\\eta|$可小于任意给定的正数$\\varepsilon$，只要$|\\Delta x|$小于某个正数$\\delta$。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "左边的积分结果: 0.24999999999999997\n",
      "右边的积分结果: 0.24999999999999997\n",
      "两边积分结果相等，定理2成立！\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import dblquad\n",
    "\n",
    "# 定义函数 f(x, y)\n",
    "def f(x, y):\n",
    "    # 选择一个连续函数，如 f(x, y) = x * y\n",
    "    return x * y\n",
    "\n",
    "# 计算定理2的左边：∫[a,b] (∫[c,d] f(x, y) dy) dx\n",
    "def left_integral(a, b, c, d):\n",
    "    # 计算二重积分的左侧：先对 y 积分，再对 x 积分\n",
    "    result, _ = dblquad(f, a, b, lambda x: c, lambda x: d)\n",
    "    return result\n",
    "\n",
    "# 计算定理2的右边：∫[c,d] (∫[a,b] f(x, y) dx) dy\n",
    "def right_integral(a, b, c, d):\n",
    "    # 计算二重积分的右侧：先对 x 积分，再对 y 积分\n",
    "    result, _ = dblquad(f, c, d, lambda y: a, lambda y: b)\n",
    "    return result\n",
    "\n",
    "# 比较定理2两边的积分结果\n",
    "def compare_integrals(a, b, c, d):\n",
    "    left = left_integral(a, b, c, d)\n",
    "    right = right_integral(a, b, c, d)\n",
    "    \n",
    "    print(f\"左边的积分结果: {left}\")\n",
    "    print(f\"右边的积分结果: {right}\")\n",
    "    \n",
    "    # 判断两者是否接近相等\n",
    "    if np.isclose(left, right):\n",
    "        print(\"两边积分结果相等，定理2成立！\")\n",
    "    else:\n",
    "        print(\"两边积分结果不相等，定理2不成立。\")\n",
    "\n",
    "# 设置积分区间 [a, b] 和 [c, d]\n",
    "a, b = 0, 1  # 对 x 的区间 [a, b]\n",
    "c, d = 0, 1  # 对 y 的区间 [c, d]\n",
    "\n",
    "# 比较两边积分\n",
    "compare_integrals(a, b, c, d)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DB2breidPnuTJJ5+kbt26uLq6sm/fPh555JFM93V1daVixYpZtmVQUBBt2rQhPDzcFpiutdHtfB6uKV++PJcvX7b9jB07Nt32V199lXvuuYfevXsTGRlpC003mvfpei4uLjccqGP06NG2a8+cOZMmTZpw+fJlRo4cyeDBgxk+fDh//fUXf/zxBwD/93//x4ABA/Dx8SEoKChbNYiIOJJCk4hIHnruuecoXbo0FStWJDY21rZ87efasz2DBg1i8+bNTJ8+nZSUlJs+83Hfffdx9erVTH/uu+8+235ZTQqb2U9wcDCXLl2iUqVKtnX9+vWjZ8+elC5dmgYNGmAYhm352k9CQoLtPXz99de8//77lC5d2jawwubNm7Ndg8lksh0XHR2dLnBkxt3dndq1a3P27FnOnj1LTEwMycnJtuWyZcve9BzXtG/fnt27d7Ny5Uq2bNlCxYoV022fN29ett9DoUKFuHTpEq1atUr3vnLr83At1Fz7uXaH6vrt8+bNo0WLFlgsFtsdseuf2boV586ds53n2rULFy6Mm5sbAQEBtjtIlSpVomfPnowcOZLly5fzxx9/8Pzzz9/WtUVE8pK654mI5KF58+YxceJE6tSpw+rVq2nTpg0A8+fPZ+LEibZuZDVr1qRZs2ZMnTqVYcOG4e/vf8Pzurm52e7CZLbtmmuTwgLExMTw9ttvM2nSpEwnFj127BgPPPAAv/zyi+1ugJ+fH2XKlOG3336jY8eO7N27l+rVqwMwdepUfvrpJwoVKgRAly5dKFasGO+88w5Tp061jczWuHHjDAMO3Ii3tzdRUVGkpqbe8G5Hamoqo0aNynQY9WvzBgFUqVKF48eP3/S6CxYsyHBX6sqVK/Tr14/PP/+cHj162AKd2Wxm8uTJjB8/Pt0odtckJCTQsGFDvvzyS9tkwdcmn7XH5yEzVapUYeHChcC/81ndKDSlpaVlOujI9Tp06EC/fv1o27YtJ06c4Pz58/z6668cOnSIevXq4erqyq5duwD44IMPqFGjBoMHD2bMmDG2z42ISH6g0CQikscWLFiAxWJh69at1K1bl8uXLzN69Gg++uijdM+YVKlShd9++y3d0NdZudY9LyvXho2+djcArMOJb9y4kfj4eFasWJHhC/S1rmGVK1ematWq6bZ9/vnneHt78/PPP1OuXDn27NnDW2+9xZo1a2z7mEwmKleuzJkzZ9K9Bx8fH9tktNl1LeRkFpri4+N5/PHH+e677zh27BizZs2ybXvrrbf4/fff+e6772zrXFwy72SRlJTEwYMHbXdHmjdvnmGfs2fPsn79elJSUvD397eFlwsXLrB7926efvppfvrppwx1xsXFAdbw9t/3bo/Pw81cq+e/d6TAOkT48uXLefXVV3n88cdvGFTDw8Px9PRkypQpxMXFUaVKFVxdXQkMDOSNN95I9yyZ2WymRIkSnDx5koSEBNtogCIi+YG654mI5LHJkyezfv16Nm/eTFBQEC1btuShhx5iwIABtn0++ugj5s+fT3BwMM8//zw7duy44Tmz2z3venfffTcbNmzg999/z3SQhmvPJmUWxubNm8dXX33F/PnzCQoKolu3bowbN45WrVrZ9hk9ejRbtmyhevXqDBw4MFt3d7Jybbjqa3e8fvzxRx5++GEeeeQRoqKiWLlyJT169MDNzY3ChQvbfjw8PHB1dU237r9BwWKxcOTIEZo0acLSpUtt7/fa+7/e2bNncXFxydBVr3Tp0vz666+Eh4fTtm1b2zND19yoLXPj83D69Ol03QEzm+z4ete61V3rqmixWADrxLV169alb9++lCtXjvbt22MymTJti9jYWCIjI6lWrRobNmzgjz/+YPHixfTp04cSJUrQpUsXqlatSmpqKp988gn169enWrVq/N///R+ff/45DRs2TBeyRUScmf6JR0TEAUqXLk2FChXYtm0b5cqVY+HChbi7uzNz5kw++ugjxo4dy/jx45k4cSJt27blvvvu45NPPknXXSw1NZWzZ88SFRWF2WwmKioq02td23bq1CkqVKiQ7ot7vXr1+Omnnzhz5gwAu3fvxmQy4eHhwaJFizCZTFneaShfvjxBQUEcPnyY0qVL89Zbb2E2m3n11Vd56aWX+OCDD/jss8/o0aMHzZo1o2XLlnz11Vc3HBDiwoULrFq1ioCAAIoWLYqHhwdnzpxh/Pjx1K9fn8DAQAD27NnDr7/+Su/evenduzft27cnMjKS8+fPc/78edv5IiIiiI+PJzQ0NN11rp/v6cKFC7zzzjsMHDiQCRMm2J73Wb58OQ888IDtmKSkJGbNmkXDhg0zHXUuKCiI9evXs27dOjw8PDh06BBJSUl4e3uzbt06gCzncbrdz0OZMmXYsGGD7XyzZs1KF6x69+5NvXr1uPfee/Hx8eG1116jbNmytnmhtm7dCkC/fv14+OGHWbhwIXXq1AHg/PnzpKSk8PXXX9vWGYbBkiVLAGt3y8wkJiYyc+ZMZs+ezblz5xg3bhyTJk3CxcWFFi1a8MQTT9CtWzeqVq3Khg0bNCCEiDg3R4xzLiJyp/rss8+Mpk2bGi4uLkaHDh2MAwcOGBaLxViyZInx0ksvGf369TMA46WXXrIdExERYbRs2dIAjO+++87Ys2ePARjHjh3L0RxHwE3nw+nTp49tX19fX9vcTNd77bXXjDp16hguLi5Gnz59jNOnTxtms9n4+OOPjalTpxrt2rUz3NzcjJkzZ9qOOXHihFGzZk3DZDIZu3btyvL6ERERhru7e7qavby8jNatWxv79u2z7RcbG5thvqTnnnsu2+0wcuRIwzD+na/q+jmMDMMwnn/+ecPHxyfdMe7u7kbDhg1t8yXdzIsvvmg71tvb2xg+fHiGfXLj8zBz5kyjQoUK6c47adIk2zxNhmEYffv2TfdeypYta/zyyy+27XPnzjVq166dbi6la5KTk4377rvPcHNzS3eOIkWKGG+++WaG/a/N02SxWIxevXoZY8eONc6dO5dpG61bt8746KOPbtqWIiKOZjKMTO65i4iIXXz++eecOnWKwYMHZ/pcz7Rp0wgODqZ3797p1qempjJz5kz+97//pZsLxx4sFgsWiyXL502mT5+OyWRi4MCBGe4OGIbB888/T8+ePWndunW6bXFxcXz55Zf873//y1YdKSkppKWl3fYIbzcTHx9vG7wit1ksFgzDyPJ3lhufh4SEBKKjoylXrtwNa0lJSSEhIQHDMDIdQVDPGImIZE2hSURERERE5AY0EISIiIiIiMgNKDSJiIiIiIjcgEKTiIiIiIjIDdxxT3xaLBbOnz+Pr6/vDSeCFBERERGRgs0wDGJjYylTpkyWk5/DHRiazp8/T/ny5R1dhoiIiIiIOImwsLAbjkJ6x4UmX19fwNowfn5+Dq3FbDazdu1aOnXqhLu7u0NrKYjUvval9rUvta99qX3tS+1rf2pj+1L72pcztW9MTAzly5e3ZYSs3HGh6VqXPD8/P6cITT4+Pvj5+Tn8A1MQqX3tS+1rX2pf+1L72pfa1/7Uxval9rUvZ2zfmz22o4EgREREREREbkChSURERERE5AYUmkRERERERG7gjnumKTsMwyA1NZW0tDS7XsdsNuPm5kZSUpLdr3UnUvtmn6urK25ubhqGX0RERCQTCk3/kZKSwoULF0hISLD7tQzDoFSpUoSFhenLqh2ofXPGx8eH0qVL4+Hh4ehSRERERJyKQtN1LBYLJ0+exNXVlTJlyuDh4WHXL9sWi4W4uDgKFy58w8m05NaofbPHMAxSUlK4fPkyJ0+epFq1amovERERkesoNF0nJSUFi8VC+fLl8fHxsfv1LBYLKSkpeHl56UuqHah9s8/b2xt3d3dOnz5tazMRERERsdI3yUzoC7bcifS5FxEREcmcviWJiIiIiIjcgEKTiIiIiIjIDSg0SYE1f/58fvnlF0eXISIiIiL5nEKTFEg//PADb775Jo0aNXJ0KSIiIiKSzyk0SYFz6tQpXnrpJVavXk2xYsUcXY6IiIiI5HNOF5oWLFiAyWRi4cKFmW7fsmULDRs2xMvLi5o1a6r7lWRQsWJFQkJCqFSpkqNLEREREZECwKlCU1JSEhMnTsxy+8mTJ+natSsdOnRg586dtG7dmh49enD69Ok8rDJ/io+Pd3QJN5UfahQRERGRO49ThaZp06bd8BmUmTNnUrVqVWbMmEHt2rX56KOPKFasGF9++WUeVumc9u3bB8DChQsZNGgQAMeOHSMtLY2EhAT8/f0JDw/PcNzevXt56qmnMqz38vIiKirKKWoUEREREXEkpwlN+/fv55NPPuG9997Lcp9NmzbRuXNn27KbmxutWrVix44deVGi0zKbzXTq1Inff//dti4uLo727duzY8cO9u7dS5kyZQgMDMxw7OrVq0lLS8vR9Q4ePIirqytFihTJ8sfb25sxY8bkSo236sqVK1SrVo1Tp05l+5h+/frx7rvv5loNIiIiInIdw8Bl27t4mGMcXUmOuDm6ALB2yxs4cCCvvPIK5cuXz3K/EydOZHhOJSgoiP3792d5THJyMsnJybblmBjrL8hsNmM2m9PtazabMQwDi8WCxWK5lbeSI4Zh2P57O9dzdXVl3LhxTJ06lf79+2MYBq+99hqtWrWiWbNmTJ48mXvuuSfTa3z77bdMnz6dmjVrcu7cOdv65ORkKlSogMlksq2bN28eDzzwABaLhUqVKnH06NEsa3r99deJioqyXfN2arxVr7/+Ol27dqVChQrZPu/LL79MmzZtGDZsGP7+/rlWS35gsVgwDAOz2Yyrq+tN97/25+e/f44kd6h97Uvta19qX/tTG9uX2td+XLbMwHXr27TwLI056X6gkEPrye7v2ClC06hRoyhevDijR4++4X5xcXH4+PikW+fj40NSUlKWx7zxxhtMmTIlw/q1a9dmOJebmxulSpUiLi6OlJSUHLyD2xMbG3vb5xg4cCAdOnRg+/btmM1mHn74YYoWLUpMTAxff/01iYmJdOrUybZ/8+bN6dy5M6dPn6Zhw4b89ttv6c5XqlQp9u/fnyE4xMTEEBcXh8VisQXQzCQnJ5OSkpJun1upcdSoUbfUHgkJCXz55ZesWLEiR+0bFBRExYoV+eKLLxg+fPgtXTu/SklJITExkS1btpCamprt49atW2fHqkTta19qX/tS+9qf2ti+1L65q2zkdu45PRuA4yW7cmbjrw6uyPqdMTscHpq++OILvv32W/bu3YuLy417C3p6emYIM0lJSRnCz/XGjx+fLozFxMRQvnx5OnXqhJ+fX4ZzhYWFUbhwYby8vG7h3eSMYRjExsbi6+ub7o5OTn344YfMmDEDgMjISFxdXdmyZQsAzz77LEeOHOHtt9/Gz8+PvXv3snbtWsaPH8+XX35JrVq1KFasGEeOHKF+/foEBAQAULRoUZo3bw5AdHQ0n3/+OX369AGgcOHCnD59mooVK2ZZU3JyMiNGjOCPP/6gUqVKrF69+pZq/O/v6JqLFy8yZswY26AgixYtomXLlixcuBB/f3/Wrl2Ll5cXjRo1Ste+S5Ys4fHHH+f48eOULl0agGHDhrF7925+/fVX/P39efDBB/nhhx944YUXbvl3kh8lJSXh7e1Nq1atsvX5N5vNrFu3jo4dO+Lu7p4HFd5Z1L72pfa1L7Wv/amN7Uvtm/tMZ3fiunAuAObGIzhjbuoU7XujmwDXc3hoev3117ly5UqGbnfDhg1j2rRpHDlyxLaubNmyhIWFpdsvLCyMypUrZ3l+T09PPD09M6x3d3fP8EtKS0vDZDLh4uJy0wCXG651Gbt2zVs1atQounTpwmuvvcbff/9NSkoKDRs2ZNy4cQwcOBA3Nzfatm1Lw4YN+fjjj4mMjCQ4OJiFCxfSpEkTXFxcMJlMVKxYkdDQ0Azn79evH4CtxkKFClGsWDFOnDiBr69vpjVduXKFK1eu8PDDD/PCCy/cUo3t27fP9NwJCQl07NiR4OBgihYtyvz581mzZg09evTgzTffZMaMGfz22280aNAgQ/sOGDCAt956izfffJOZM2cyadIkNmzYwI4dOyhatCgATZo0Yfr06ZjN5kw/OwXVtc9BZn82biSn+0vOqH3tS+1rX2pf+1Mb25faN5dEnYFvhkBaMtzVDdpPgp9/cYr2ze71HR6a1q9fn6EvYY0aNXj99dfp2bNnuvUtWrRg3bp1TJ48GbCGnM2bN/Piiy/atcaElKy7KrmYTHi5u97yvokpabilpKYLTT4eOfu1TJkyhVWrVvH2229z9uxZLl26RNeuXfn444959913Wbx4MXv27KFhw4bs3r2bOnXqMG7cOFuouObvv//O9O7R5cuXeeihh2zLlStXpm3btgQGBtqey8qMYRi0bduWvn373lKNWXn33XdJSkpi4cKFTJ8+nZYtW9K6dWs6derE3r17ATh9+jRlypTJcKzJZOL111+nV69elCpVipkzZ7J161bKli1r26dMmTKkpKRw8eJFKlSokGUdIiIiInITSTGwuC/EX4ZStaHn/4HLzZ+ddjYOD01VqlTJdH3p0qVt3eiGDRtGv379+N///kfjxo2ZOnUqPXv25JNPPsFisTB06FC71nj3q1lPoNv2rhLMfbSxbbnhtPUkmjMfja5JpWIse7KZbbnVW5uJTMj48NmpN7vlqL6xY8cyadIkvvvuOz744AP++usvANsocGfPnmXx4sU89thjrF27lqVLlxIREcHgwYOZPn267TxVqlS54Z2ma0wmE19//bXda8zK8uXLGTp0KN7e3uzZs4e6deva6rp25ysxMTHLLmbdu3fn7rvvZurUqaxdu5aaNWum2+7t7Q1kv4+riIiIiGTCkgYrHoPww1C4FPRfBp6FIR8OsOE0Q45nxmw2c/jwYc6fPw9A/fr1WbJkCfPnz+eee+7h4MGDrF27NssuYneK8ePHU6pUKQYNGkRISAilSpWiVKlSNG5sDXOdOnVi06ZNvPvuu5hMJu69917efffdDM+CXbvT9N+fH3/8MUf1bN26lb59+952jZlJTEzkwIEDtqC0d+9e6tWrB8Du3bttxwUEBHD16tVMz/Hzzz8TGhpKWloaJUuWzLA9MjISgBIlSuTofYuIiIjIddZOgGNrwc0L+i8G/7I3P8ZJOfxOU2au7/J19uzZdNt69epFr1698rSew1Pvy3Kby38GcNg1sUO2993yYhtiY2Lx9fO9rWeaPvzwQ+6++26+//571qxZA8CMGTM4fvw4AEWKFGHo0KGMHTuW999/P8tBJ7Jzp6lTp062ARyyYrFYSE1N5fvvvwegXbt2rFmzJldqvDaqW3JyMpcvX+bcuXPUrVuX3377jZMnT9q6dNavX5+FCxdmOH737t306dOHOXPmMG/ePCZOnMjy5cvT7XPw4EHKlStnGxRDRERERHLory9hxyfW1z1mQ9mGjq3nNjllaHI2OXnGKKf7pnq44uPhdtsDT0RHRxMaGsrkyZOpVasWs2fPTjeM+LWRQQoVynos/Ow807R27VoA4uPjeeCBB/j4448JDg5Ot/+qVauYMGGC7fmi3KzR19eXevXq8dFHHxEbG4u7uzvHjh1j5MiRTJ8+3Vb/fffdx/jx44mKirKNwHfq1Cm6devGyy+/TP/+/alcuTLNmjVj9+7d6Z7v2rp1a7qhz0VEREQkB/7eBKvHWF+3mwA1ezi2nlzg1N3zJPtefPFFNm/ezPz58+nduze1atWyTdb70ksv8fPPP/Phhx/y7LPPsmjRokzPUaVKFU6dOpXh5/7778+wb6FChejatSv33nsv27dvz7MaARYsWEB8fDzDhw8nNTWV559/nvHjxzNmzBjbPrVr16ZBgwZ89913gLXLXefOnXnwwQcZN24cYB0lr0uXLrz88su245KSkli5cuUdN0eTiIiISK64fAS+fgSMNKjTF1qOufkx+YDuNBUAW7duZfny5SxbtoyHHnqIZ599llmzZvHWW29x/vx5/vjjD9auXUvt2rXx9/fn0UcfZf/+/ZmGoZx44YUXcHFxISoqitjYWK5cuYKXlxcbNmzI8LzUrdZ4bW6n69WqVYvdu3czYMAAfH19+eyzzzKtb8KECYwdO5Znn32WYsWKZdr1cPXq1emW586dS+PGjWnatOlttIyIiIjIHSg+Ahb1huRoCGoGD8yE25iL1JkoNBUABw4coEyZMuzcuZOgoCAAZs+ezdWrVxkzZgy7d++mVKlSADzyyCNUq1aN5ORk2/FTpkzh3XffJT4+niJFimQ4f0JCAj/++CNbtmzhk08+Sbdt1KhRAPz55580adIEAD8/P2bNmpWrNWbm4MGDPPnkk1lu79atGwcPHuTcuXPZHjrc3d2dmTNnZmtfEREREfmHOQmWDoCo01C0IvRdBG4FZ75LhaYCYMSIEZmuL1q0KHPmzMmw/vqR6TZv3gzApEmTbquGxo0bk5aWhmEYuLpmHHv/dmrMTGpqKkeOHKF27do33O/pp5+2PdOUHY8//ni29xURERERwDDg+5EQ9gd4+cOA5VCouKOrylUKTZJrbncwi5xwc3O76Z0oEREREckDm9+Eg9+Aixv0WQAlqju6olyngSBEREREROTW7P8afn3T+rr7+1C5tWPrsROFJhERERERybnT263d8gCaPw8Nhji0HHtSaBIRERERkZy58jcsHQhpKVDjfmh/e8/HOzuFJhERERERyb6ESFjcBxIjoUx96PF/kIfPtjtCwX53IiIiIiKSe1KTYdkguHIc/MtD/6Xg4XPz4/I5hSYREREREbk5w4AfnoXTv4GnHwz4GnxLObqqPKHQJCIiIiIiN/frDNi/DEyu0HselLzb0RXlGYUmERERERG5sX3LYPMb1tfd34Oq7R1bTx5TaBIRERERkayd2pZ+aPGGQx1ZjUMoNImIiIiISOYijlmHFreY4e6HCvzQ4llRaJI7TocOHTh27JijyxARERFxbvERsKgXJEVBuUbQY3aBH1o8K3fmu5Y72rFjx6hSpYqjyxARERFxXuZEWNIfrp6CIhWg3xJw93Z0VQ7j5ugCROzt0KFDPP744yQmJtK3b19KlSqFyx36ryQiIiIiN2WxwHdPwtk/wcsfBi6HwiUcXZVD6ZujFGjJycn079+fL774gv3797Nz507q1Knj6LJEREREnNf6V+Hw9+DqAf0WQ4m7HF2Rwyk0Sb63dOlSypYtS3BwMPv27Uu3bfXq1bRq1YratWsDUKNGDYUmERERkaz8+Tlsn2l9/eAnULGFY+txEgpNkq+FhYUxdOhQqlatioeHB0899VS67YcPH6Zu3bq25V27dik0iYiIiGTmyM/w04vW1+0mQJ3ejq3HieiZJnEa8fHxFCpUKEfH7Nixg+TkZCZOnIjZbGbFihWkpaXh6uoKQNGiRTl06BAAa9euZf369SxbtizXaxcRERHJ187vgW8eBcMCDYZAyzGOrsip6E7THezNN99kz549GdbHxcVRqlQpnn/++Vy93rWucwsXLmTQoEGAdSS7tLQ0EhIS8Pf3Jzw8PEfnPHfuHAClS5emS5cufPHFF7bABNCnTx9+++036tevz4IFC6hQoQJFixbNpXckIiIiUgBEnYHFfcGcAFXaQbf3wGRydFVORaGpgHrqqafw8fGhSJEi+Pj44OnpSZEiRShcuDBt2rQBIDU1lS5dunDixIl0x06fPp2goCDmzp3L33//neHcBw8exNXVlSJFimT54+3tzZgx//4LhdlsplOnTvz++++2dXFxcbRv354dO3awd+9eypQpQ2BgYI7eZ1xcHACFCxfOdHuJEiXYuXMne/bsYcGCBZw8eTLDPjNnzqRChQq4ubmlq/m/rly5QmBgIKdOncpRjbeqX79+vPvuu9ne/7XXXqNp06Z2rEhEREQKnMQoWNQb4i5ByVrQ+ytwdXd0VU5HoakA6NKlC4ULF8ZkMlG4cGHbHETvvfceUVFRvPXWWwwfPpyoqChWrVplO27ChAm0aNGCRx991LZuw4YNzJ49m6+//ppRo0bRq1cvEhISMlyzUqVKREVFZfnzyiuvpNvf3d2d8ePHM23aNNu6119/ndatW9O8eXN++eUXGjVqlOP3frPQdDP79u1j9OjRfPrpp4SFhTF16tQs93399dd58MEHqVix4i1dK6cmTJjA66+/TnR0dLb237dvH/Xq1bNvUSIiIlJwpKbAskFwORR8y8CAr8HLz9FVOSWFpgLgp59+Ii4ujuLFi3Pq1KlM7w5lZc6cOXz55ZcA/P777/Tu3ZsFCxZQsWJFJk6cSIkSJejevTsxMTG3XeeIESOYPXu2bXno0KG89957ACxfvpzdu3fTuXNn28+bb75503PebmhatWoVjRs3pmvXrpQuXRofH59M90tISGDOnDk89thjt3SdW1GrVi2qVKnCwoULs7W/QpOIiIhkm2HAD8/Aqa3gURgGfg3+ZR1dldNSaCrAxo8fT7ly5Zg4cSLz5s2jXLly9O6dfhQUf39/2xfzLl268PHHH9OtWzcAXF1dWbFiBUlJSTRq1Iht27bZjjt58uQNu+e9/vrrAKxbt47jx4/zwQcfEBQUROPGjRk2bBgrVqygdevW1K5dm+nTpxMSEsIzzzxDr169qFKlCsePH6dJkyY3fY9xcXG4u7vj6emZ4/apWrUqEyZMYPv27ZhMJoYMGZLlvmvWrMHT0zND97clS5bg7e3NhQsXbOseffRR6tSpc9M7ROXKleOTTz5Jt2779u34+Phw+vRpAO6//36WLl2a4dhdu3bRqlUrvL29qV+/Pn/88Qd///23LTRl59wiIiJyB9s4DfYvAxc36DMfStV2dEVOTaGpAHvjjTc4e/Ys06ZNY+jQoZw9e5bly5cD0LRpU0wmEyaTiejoaObMmcM333xD//79053D19eXdevWUbduXduzPN7e3hQrVoywsLAsu+edPXuWJ554gtGjR7Nt2zaef/55Nm/eTIcOHWjYsCF33303DzzwANu3b+fHH3/Ezc2NNm3a8Pjjj3P33Xdzzz330LZt25u+x9jY2Fu+y7R9+3YqV67M22+/zYULFzKEjOtt3bqVhg0bZljfr18/qlevzvTp0wGYNGkS69ev56effsLf3/+G12/SpAk7d+60LRuGwfPPP8+oUaOoUKECAI0bN+bPP/8kOTnZtl9oaCht27aldevWHDx4kAkTJvDQQw8B2IZTz865RURE5A7111zY+s9z0/d/CFXbO7aefEBDjt+IYVhHEbEXi8V6/hRXcPlPfnX3yfaoJZMmTWLFihVERUXRsmVL6tatS5EiRW54zG+//UZqaipeXl54enqyadMmYmJi6NChA+vXr7ftt3z5cjZv3szXX39tW1e5cmXatm1LYGAghmFkeQ3DMGjbti19+/ZlypQprFq1irfffpuzZ89y6dIlunbtyscff8y7777L4sWL2bNnDw0bNmT37t3ZnkspLi7ulkNT4cKFOXXqFC1atKBUqVI33Pf06dOUKVMmw3qTycTrr79Or169KFWqFDNnzmTr1q2ULXvz29tNmzblq6++si0vWLCAsLAwxo8fb1tXpkwZUlJSuHjxoi3sjBw5koceesj2fFiVKlVYunQpBw4csHUvzM65RURE5A509BdYPdr6uvU4qD/IsfXkEwpNN2JOgOkZvyjnFhegSFYbXz4PHtmbs2jYsGHcf//9dOjQgVmzZlGmTBk+/PBDxowZw4QJE0hKSiItLY2lS5diNpupX78+rq6uGQJPSkoKGzZsACA8PJwJEybwyy+/sGTJknT7mUymdCEqO8aOHcukSZP47rvv+OCDD/jrr78AbKPDnT17lsWLF/PYY4+xdu3aTLukZeZ2QtP+/fsBqF375rejExMT8fLyynRb9+7dufvuu5k6dSpr166lZs2a2bp+06ZNGTduHHFxcZhMJl5++WVee+21dO/H29sbwDYYx+nTp9m4cSO7d+9Ody53d/d0zzNl59wiIiJyhzm3G5YPtc7FVG8QtBnn6IryDXXPKwAqVKjAPffcg5ubG3Xr1qVGjRq8//77REZGEhERwZtvvsljjz1GREQEV65cSTeCXmZefvllqlatSkJCAnv37uXee+/NUT1bt26lb9++6daNHz+eUqVKMWjQIEJCQihVqhSlSpWicePGAHTq1IlNmzbx7rvvYjKZsn3N2wlNe/fupWrVqtmaUDcgIICrV69muu3nn38mNDSUtLQ0SpYsme3rN2zYEBcXF3bv3s2MGTMoUaJEupEMASIjIwHr0OnXanZzc8sQ9Pbs2ZMuNGXn3CIiInIHuXoKFvf5dy6m+z/QXEw5oDtNN+LuY73jYycWi4WY2Fj8fH1xyax73i1KTk7mnnvusT3wbzabMQyDefPm2fa5dOlSloMn7N69my1btti+hMfGxnLx4kWqVatGp06d2LJly03fV2pqKt9//z0A7dq1Y82aNdx99918//33rFmzBoAZM2Zw/PhxAIoUKcLQoUMZO3Ys77//PqZs/iG+Nmrgrdi7dy9169ZNt6558+a89957NGnShMcee4xatWoxatQo6tevn+kodrt376ZPnz7MmTOHefPmMXHiRNtzYzfj4+ND7dq1WbFiBZ9//jlr1qzJ8Dk4ePAg5cqVIyAgAAAXFxcsFgspKSm4uVn/+K5Zs4bQ0NB0oSk75xYREZE7REIkLOwF8ZehZG3NxXQLFJpuxGTKdhe5W2KxgHua9Rq3+YU2NDSUlJQUHnroIc6fP59uwtpZs2YRGhrKrFmz0h2Tmpqa6euff/453X4hISE8+OCDXLhwgbVr1wIQHx/PAw88wMcff0xwcHC6/VetWsWECRPYu3dvuvXR0dGEhoYyefJkatWqxezZs/ntt99s268Na56dOz/XxMXF4evrm+39r7d3714eeOCBdOsmTpzIm2++ScuWLXFxcWHUqFEA3HfffYwfP56rV69StGhRAE6dOkW3bt14+eWX6d+/P5UrV6ZZs2bs3r2bBg0aZKuGpk2bMnPmTB588EHbpMPX27p1K506dbItN2zYEHd3d8aOHcsLL7zAwYMHefrppwEyDDd+s3OLiIjIHcCcBEsHwJVj4FcOBi7XXEy3QP/0XAC0adOGevXqce+999KvXz82bdqUo+N3795Njx49stx+4cIFKlWqlG5doUKF6Nq1K/feey/bt2/P1nVefPFFNm/ezPz58+nduze1atWy3QV76aWX+Pnnn/nwww959tlnWbRoUbbOeauj51ksFg4cOJDhTlPnzp05c+YMq1evTjeaXu3atWnQoIHtWa7IyEg6d+7Mgw8+yLhx1v7ATZo0oUuXLrz88su24+bNm3fDu2Z169bF3d2dt99+O8O2pKQkVq5cyfDhw23rypQpwxdffMEPP/xAzZo1effddxkyZAglS5bMMJjFjc4tIiIidwBLGnw7HM78Dp7+1sDkV9rRVeVLutNUAHz88cdUqFDBFh6eeuqpdF3JMuue169fP1599VUAunXrxjvvvGMbdOC3336zDa+dmJjI0qVLMx0s4YUXXsDFxYWoqChiY2O5cuUKXl5ebNiwIcMksVu3bmX58uUsW7aMhx56iGeffZZZs2bx1ltvcf78ef744w/Wrl1L7dq18ff359FHH2X//v3MmDEjy/dtsVhITEy8pdDk4uJCfHx8hvU7d+4kMjKSChUq4O6e/rb1q6++ytixYxk+fDjFihUjNDQ0w/GrV69Ot3zy5Elat26dZR1Lly7lmWeeoWrVqhm2zZ07l8aNG2eYG2rQoEEMGpR+pJs33ngjR+cWERGRAs4w4OfxEPIDuHpAv0VQ8m5HV5VvKTQVAP8drW327NnMnj37psetW7eOu+66ixUrVtjO8cgjj9CmTRtbdz1XV1fq1KmT5XM617qv/fnnn7bJaP38/DJ0BTxw4ABlypRh586dBAUF2eq8evUqY8aMYffu3bY7JY888gjVqlVLNzfR9ebPn0+pUqWoX78+8O8gCbfr3LlzPP7442zcuJGHH36YgwcPUqtWLdv2bt26cezYMc6dO0f58uWzdc6ffvopQ1tYLBYuX77MnDlzOHbsmO3Zr/9yd3dn5syZOXoP2T23iIiIFHDbP4I/P7O+7jEbKrV0bD35nELTHaxjx47s27cv3YAQ8+bNS3dHKrsaN25MWloahmHg6uqaYfuIESMyPa5o0aLMmTMnw/objZ737bffcvToUduEro0aNcpxvf+VmJhI7969mTlzJpUqVWL8+PFMmzaNZcuWpdvv+eefz9F5//zzzwzrtmzZQrt27QgODmbFihX4+WXer/jxxx/P0bVycm4REREpwPYvh3XWHkV0eh1qPezYegoAhaY7XFYj6N2KvBqdbfLkybRv35433niDgQMHZhjM4ZrTp0/z9NNPc+nSJcxmM2vWrLHd5fovb2/vdM9m9e7dm969e9ul/jZt2mCxWPLduUVERCQfOLEZVloHiaLpSLj3GYeWU1AoNEm+U69ePc6cOUNkZGSW3eRSUlLo3r07M2bMoGvXrkRHR2tiVxERESnYLh6EZYPBYoaaPaDTa46uqMBQaJJ8qVChQjccmvy7776jSZMmtGjRAsA2TLiIiIhIgRQVBot6QXIMVGgOD82+7Slt5F9O05LLli2jbt26+Pj4EBQUxGuvvYZhGBn2S0tLw8XFBZPJZPvRHQT5rwMHDuTKs04iIiIiTi8h0hqYYi9AiRrWkfLcvRxdVYHiNHeaQkNDGT9+PHfffTe///47I0eOJCAggKeeeirdflevXsUwDDZv3kzZsmWBvHuWRvKPkiVLcujQIcAatKOioihWrJiDqxIRERHJZeZEWNIfLoeCbxkY9A14q4dNbnOa0DRp0iTb6zp16vDDDz+wdu3aDKEpMjISgAYNGuDr65unNUr+MXToUPr06UOzZs3w8vLi008/zTDfkYiIiEi+ZkmDFY9D2A7r5LWDVoB/OUdXVSA5TWj6L4vFQvHixTOsj4yMxMPDI9uBKTk5Od18PzExMYB1wlez2Zxu32uTwFosljwZgexa98Nr15TcU6hQIVatWkVsbCy+vr6YTCa18U1YLBYMw8BsNmc6bPx/Xfvz898/R5I71L72pfa1L7Wv/amN7StftK9h4PLTGFxDV2G4epLWZwFGsWrgzDX/w5naN7s1mIzMHhxyoPj4eJYuXcqYMWP49ddfqVOnTrrtq1evpnv37nh5eREYGEjz5s2ZPn06FStWzPR8kydPZsqUKRnWL168GB8fn3Tr3NzcKFWqFOXLl8fDwyPX3pNIfpCSkkJYWBgXL160TW4sIiIizqn6xZXUuPAtBiZ2VnqGC0X0LPetSEhIYMCAAURHR99wfkunCk1eXl4kJyfj6+vLp59+ysCBAzPsExERwcmTJ/H09CQ0NJQpU6aQkJDA/v37M737lNmdpvLlyxMREZGhYZKSkggLC6NixYp4edn/4TnDMNLdCZHcpfbNmaSkJE6dOkX58uWz9fk3m82sW7eOjh074u7ungcV3lnUvval9rUvta/9qY3ty9nb17RnAW5rRgGQdt9bWO4Z5uCKcsaZ2jcmJoaAgICbhian6p63d+9eoqOj+euvv3juuec4dOgQ06dPT7dPQEAAAQEBgPXZp6ZNm1KxYkV+/vnnTCcj9fT0zHQCV3d39wy/pLS0NEwmEy4uLnkyuMS17mLXrim5S+2bM9dGpczsz8aN5HR/yRm1r32pfe1L7Wt/amP7csr2PfIT/PSC9XXLMbg2e5Kbd6p3Ts7Qvtm9vlOFpuDgYACaNGmCj48Pw4cPZ+LEiXh7e2d5TFBQEMWLF+f06dN5VaaIiIiISN4L+xOWPwqGBeoNgnYTHF3RHcNp//ndzc0NwzBIS0u74X4nTpwgIiKCqlWr5tq1najHokie0edeRETEiV0+Cov7QGoiVOsE938AevwgzzjFnaaYmBieeeYZBg0aROnSpdm3bx8vvvgi/fv3x8PDg06dOjFs2DD69evH3LlzSU1NpXHjxoSFhTFu3Djq1KlD9+7db7uOa7fnEhISbnh3S6QgSkhIALJ/m1pERETySPQ5WNADEq9C2YbQex646v/XeckpQpOXlxdms5khQ4YQHR1NhQoVePbZZ3nhhRcwm80cPnyY8+fPA+Dv78+YMWM4f/48pUuXpmvXrrz++uu4ud3+W3F1daVIkSKEh4cD4OPjY9cBBCwWCykpKSQlJemZGztQ+2aPYRgkJCQQHh5OkSJFsjXcuIiIiOSRhEhY2BNizkLxajBgOXgUcnRVdxynCE0eHh4sWbIk022enp6cPXvWttyzZ0969uxpt1pKlSoFYAtO9mQYBomJiXh7e2t0NztQ++ZMkSJFbJ9/ERERcQIpCbCkH1wOBd/SMPhbKJRxHlOxP6cITc7EZDJRunRpAgMD7T7hltlsZsuWLbRq1UpdouxA7Zt97u7uusMkIiLiTNJS4ZtHIewP8PKHQd9CkSBHV3XHUmjKgqurq92/RLq6upKamoqXl5e+1NuB2ldERETyJcOAH5+Doz+Dmxf0XwYl73Z0VXc0PeghIiIiIuJMNkyBvQvB5AK95kKFZo6u6I6n0CQiIiIi4ix+/wS2vW99ff+HENzVsfUIoNAkIiIiIuIc9i+HX8ZbX7d/FRoMcWw9YqPQJCIiIiLiaMfWwcqnrK+bPAUtRju2HklHoUlERERExJHC/oRlg8GSCrV7w31vgKZLcSoKTSIiIiIijhIeAot6Q2oiVO0AD34CLvqK7mz0GxERERERcYSrp2FBD0iKgnKNoc98cPNwdFWSCYUmEREREZG8FnfZGphiL0CJGjBgGXgUcnRVkgWFJhERERGRvJQUA4sehsi/wT8IBn8LPsUcXZXcgEKTiIiIiEheMSfB0gFwYR/4BMDg78CvjKOrkptQaBIRERERyQtpqbDiMTi1FTx8YdA3EFDV0VVJNig0iYiIiIjYm2HAj89B6Cpw9YT+i6FMfUdXJdmk0CQiIiIiYk+GAWsnwN6FYHKBXl9CpVaOrkpyQKFJRERERMSetr4Lv8+yvn5gFtTo7th6JMcUmkRERERE7GXnHNg4zfr6vulQf6Bj65FbotAkIiIiImIPB76B1S9YX7caC81GOrYeuWUKTSIiIiIiue3YevjuScCARo9D21ccXZHcBoUmEREREZHcdGYHLBsEllSo1Qu6vA0mk6Orktug0CQiIiIiklsu7INFvSE1Eap2hB6zwUVfufM7/QZFRERERHJDxDFY0BOSYyDoXugzH1zdHV2V5AKFJhERERGR2xUVBvMfgoQIKF0XBiwFDx9HVyW5RKFJREREROR2xIXD/Ach5iwEVIdB34KXv6Orklyk0CQiIiIicqsSr1q75EX+Df5BMHglFApwdFWSyxSaRERERERuRUo8LOoDlw5AoUAYshL8yzq6KrEDhSYRERERkZxKTYalA+Hsn+BVxBqYildxdFViJwpNIiIiIiI5kZYK3wyDE5vAvRAMWgElazq6KrEjhSYRERERkeyyWOD7kRC6Clw9of9iKHePo6sSO1NoEhERERHJDsOANS/A/qXg4gZ9voLKbRxdleQBhSYRERERkZsxDFj3Kvz1JWCCHp/BXV0cXZXkEYUmEREREZGb2fI2bP/I+vqBj6B2L8fWI3lKoUlERERE5EZ+/wQ2vW59fd8b0GCIY+uRPKfQJCIiIiKSlV1fwS/jra/bvgLNRji2HnEIhSYRERERkUyYDq2AH5+zLtz7P2g11rEFicO4OboAERERERFnUzrqL1z3fgwYcM9j0HEqmEyOLkscRHeaRERERESuY/p7A/ec+hiTkQZ1+kHXdxSY7nAKTSIiIiIi15zcgus3j+BipGGp8SA8+DG46CvznU6fABERERERgDN/wOJ+mFKTuOBXn7QHPwVXPc0iCk0iIiIiInB+DyzqBeZ4LJXa8FelkeDq4eiqxEk4TWhatmwZdevWxcfHh6CgIF577TUMw8h03y1bttCwYUO8vLyoWbMmv/zySx5XKyIiIiIFxqXDsKAHJMdA0L2k9foKi4sCk/zLaUJTaGgo48ePZ8eOHbzyyitMnjyZzz77LMN+J0+epGvXrnTo0IGdO3fSunVrevTowenTpx1QtYiIiIjkaxHHYP6DkHgVyjaEAcvAo5CjqxIn4zShadKkSfTr1486derw5JNPct9997F27doM+82cOZOqVasyY8YMateuzUcffUSxYsX48ssvHVC1iIiIiORbkSfgqwcgPhxK1YZBK8DLz9FViRNymtD0XxaLheLFi2dYv2nTJjp37mxbdnNzo1WrVuzYsSMvyxMRERGR/CzqjDUwxZ6HgLtg8ErwLuroqsRJOd1wIPHx8SxdupQdO3bw66+/Zth+4sQJKlWqlG5dUFAQ+/fvz/R8ycnJJCcn25ZjYmIAMJvNmM3mXKw8565d39F1FFRqX/tS+9qX2te+1L72pfa1P7XxbYq5gNuC+zFFh2EUq0zqgBXg4Q//aVe1r304U/tmtwaTkdVoCw7g5eVFcnIyvr6+fPrppwwcODDDPq6ursybN4/Bgwfb1k2dOpX58+dz/PjxDPtPnjyZKVOmZFi/ePFifHx8cvcNiIiIiIhT8zRH0eLYdAonXyTeowTbqr1CkkcxR5clDpKQkMCAAQOIjo7Gzy/rrplOdadp7969REdH89dff/Hcc89x6NAhpk+fnm4fT09PUlJS0q1LSkrKMgCNHz+e0aNH25ZjYmIoX748nTp1umHD5AWz2cy6devo2LEj7u7uDq2lIFL72pfa177Uvval9rUvta/9qY1vUXwEbosewpR8EcOvHB6Df6BdkaAMu6l97cuZ2vdaL7SbcarQFBwcDECTJk3w8fFh+PDhTJw4EW9vb9s+ZcuWJSwsLN1xYWFhVK5cOdNzenp64unpmWG9u7u7w39J1zhTLQWR2te+1L72pfa1L7Wvfal97U9tnAMJkbCkN1wOBd/SmB75AffiVW54iNrXvpyhfbN7facdCMLNzQ3DMEhLS0u3vkWLFqxbt862nJaWxubNm2nfvn1elygiIiIi+UFSNCzsCZcOQKFAGPID3CQwiVzPKUJTTEwMQ4YMYe3atRw4cICFCxfy4osv0r9/fzw8POjUqRNLly4F4H//+x9//vknU6dO5eDBgzz77LNYLBaGDh3q2DchIiIiIs4nORYW9oLze8C7GAz5HkpUd3RVks84Rfc8Ly8vzGYzQ4YMITo6mgoVKvDss8/ywgsvYDabOXz4MOfPnwegfv36LFmyhHHjxjF9+nQaN27M2rVr8fX1dfC7EBERERGnkhwHi3rD2T/By98amEre7eiqJB9yitDk4eHBkiVLMt3m6enJ2bNn063r1asXvXr1yovSRERERCQ/SomHxX3hzO/g6W+dh6l0HUdXJfmUU3TPExERERHJNSkJsKQfnN4GHr4w+Fso28DRVUk+ptAkIiIiIgWHOQmWDoCTW8CjMAxaAeXucXRVks8pNImIiIhIwZCaDMsGwYlN4O4DA5dDUBNHVyUFgEKTiIiIiOR/qSnw9RA4vg7cvGHA11DhXkdXJQWEQpOIiIiI5G9pZvjmUTj6M7h5wYClUKmlo6uSAkShSURERETyr2uBKXQVuHpCv8VQuY2jq5ICRqFJRERERPKnNDN8MwxCfgRXD+i3CKq2d3RVUgApNImIiIhI/pNmhhWPQcgP1sDUdxFU6+joqqSAUmgSERERkfwlLRVWPA6HvwcXd+i7EKp3cnRVUoApNImIiIhI/pGWCt8Oh8MrrwtM9zm6KingFJpEREREJH9IS4XvnoBD3/4TmBbAXZ0dXZXcARSaRERERMT5paXCyqfg4AprYOozH+7q4uiq5A7h5ugCRERERERuKC0VvnsSDn4DLm7Q5ysI7uroquQOotAkIiIiIs7rWpe8gyusgan3VxDczdFVyR1GoUlEREREnFNaKnz7OBz67p8ueQpM4hgKTSIiIiLifNLM/wwrvvLfZ5jUJU8cRKFJRERERJxLmhm+GfbvxLV9NEqeOJZCk4iIiIg4jzQzfPMohPxoDUyah0mcgEKTiIiIiDiH1BRrYApd9U9gWgTVOzm6KhGFJhERERFxAqnJsHwoHFkDrp7QbzFU6+DoqkQAhSYRERERcTRzEnw9GI6tBTcv6LcIqiowifNQaBIRERERxzEnwtIB8PdGcPOG/kugSltHVyWSjkKTiIiIiDhGSgIs6QcnfwV3HxjwNVRq6eiqRDJQaBIRERGRvJccB4v7wult4FEYBi6HCvc6uiqRTCk0iYiIiEjeSo6FRb3hzO/g4QuDVkBQE0dXJZIlhSYRERERyTtJ0bCwF5z9Ezz9YfC3UO4eR1clckMKTSIiIiKSNxIiYWFPOL8HvIrA4O+gbANHVyVyUwpNIiIiImJ/8RGw4CG4eAC8i8GQlVC6rqOrEskWhSYRERERsa/YSzD/QbgcAoVKwJAfoOTdjq5KJNsUmkRERETEfmLOw1f3w5Xj4FvaGphKVHd0VSI5otAkIiIiIvYRdcYamK6eAv/y8MgPUKyyo6sSyTGFJhERERHJfZEn4KsHIDoMilaER36EIkGOrkrklig0iYiIiEjuijhmvcMUewGKV7UGJr8yjq5K5JYpNImIiIhI7rl40DpKXvxlKFEDhnwPviUdXZXIbVFoEhEREZHccW4XLOgJSVFQqjYMXgmFAhxdlchtU2gSERERkdt3+ndY1BtSYqFcIxj4DXgXcXRVIrlCoUlEREREbs/fm2DpADAnQMWW0H8JePo6uiqRXKPQJCIiIiK37sjP8PUQSEuGqh2gzwLw8HF0VSK5ysXRBYiIiIhIPnXoO1g20BqYgrtDv8UKTFIgKTSJiIiISM7tXQzfDANLKtTuDb3ngZuno6sSsQuFJhERERHJmT8/h5VPg2GBBkOgx2fg6u7oqkTsxilC0759++jUqRM+Pj6UKlWKRx99lCtXrmTYLy0tDRcXF0wmk+2ncOHCDqhYRERE5A619V1YM8b6usnT0P1DcHF1bE0iduYUoenpp5+mTZs27Nixgzlz5vDrr78yZMiQDPtdvXoVwzDYvHkzx44d49ixY+zfv98BFYuIiIjcYQwD1k+GDVOty61ehM5vgItTfJ0UsSunGD1v6dKlBAUFAVCnTh2io6MZPHgwCQkJ+Pj8+zBhZGQkAA0aNMDXV8NYioiIiOQJiwV+Ggs7v7Aud5wKzZ9zbE0iecgpQtO1wHSNl5cXFoslw36RkZF4eHjkKDAlJyeTnJxsW46JiQHAbDZjNptvseLcce36jq6joFL72pfa177Uvval9rUvta/95WkbW1JxXfU/XA58jYEJS5e3sTQYCgX496vPsH05U/tmtwaTYRiGnWvJEcMw6N69O1euXGHHjh3ptq1evZru3bvj5eVFYGAgzZs3Z/r06VSsWDHL802ePJkpU6ZkWL948eJ0d7FEREREJD0Xi5mGpz6hTPQuLLiwu8ITnCt2r6PLEsk1CQkJDBgwgOjoaPz8/LLcz6lCk9lsZsSIESxatIgtW7Zwzz33pNseERHByZMn8fT0JDQ0lClTppCQkMD+/fuzvPuU2Z2m8uXLExERccOGyQtms5l169bRsWNH3N014kxuU/val9rXvtS+9qX2tS+1r/3lSRunxOO6YiguJzZhuHqQ1uMLjLu62udaTkafYftypvaNiYkhICDgpqHJKbrnAZw9e5a+ffty8uRJNm/enCEwAQQEBBAQEABYn31q2rQpFStW5Oeff6Z3796ZntfT0xNPz4xzBri7uzv8l3SNM9VSEKl97Uvta19qX/tS+9qX2tf+7NbGiVdhaV8I+wPcfTD1W4xblba5fx0np8+wfTlD+2b3+k4Rmo4ePUrbtm2pU6cO+/bto0SJEtk6LigoiOLFi3P69Gk7VygiIiJyh4i9BAt7wqWD4OUPA7+B8o0dXZWIQzlFaBowYACtW7dm4cKFuORg2MoTJ04QERFB1apV7VidiIiIyB3i6mlY8BBEnoBCgTD4OyhVy9FViTicw0PTsWPH2LVrF+PGjePEiRPptpUoUYLevXszbNgw+vXrx9y5c0lNTaVx48aEhYUxbtw46tSpQ/fu3R1UvYiIiEgBcfkIzH8IYs9DkSAYvBKKV3F0VSJOweGh6cKFCwCZPpP0wQcfcPjwYc6fPw+Av78/Y8aM4fz585QuXZquXbvy+uuv4+bm8LchIiIikn+d2w0LH4bESCgRbL3D5FfG0VWJOA2Hp41WrVpxowH8nnvu34nTevbsSc+ePfOiLBEREZE7w6ltsLgfpMRCmQYwaAX4FHN0VSJOxeGhSUREREQcJHQNLB8KaclQsSX0XwKemU/jInIny/6oCyIiIiJScOxZBMsGWQPTXd2so+QpMIlkSqFJRERE5E6zfSZ8PwKMNKg3EPrMB3cvR1cl4rTUPU9ERETkTmEYsGEKbHvfunzvs9BxGphMjq1LxMkpNImIiIjcCSxpsGoU7P7KutxhCrR43qElieQXCk0iIiIiBV1qMqx4HEJ+AJMLdP8AGj7i6KpE8g2FJhEREZGCLDkWlg6Ek7+Cqwc8PAfufsDRVYnkKwpNIiIiIgVV3GVY9DBc2AcehaHfIqjcxtFVieQ7Ck0iIiIiBdHVU7CgB0SeAJ8AGLgcyjZwdFUi+ZJCk4iIiEhBc/EALHwY4i5BkSAYvBKKV3F0VSL5lkKTiIiISEFyahss6Q/JMVCylnXSWr/Sjq5KJF9TaBIREREpKEJ+hG8eg7RkqNAc+i0G7yKOrkok31NoEhERESkIds2zzsNkWCC4Ozz8Bbh7O7oqkQJBoUlEREQkPzMM+PUt2DzdutxgCHR7H1z1NU8kt+hPk4iIiEh+ZUmDVWNh11zrcssx0G4CmEyOrUukgFFoEhEREcmHXCwpuK4YCkd/AkzQ9W1oPNzRZYkUSApNIiIiIvlN4lXuPT4Dl/hj4OppfX7p7gccXZVIgaXQJCIiIpKfRIXhtrAnxeOPYXj5Y+q/FCrc6+iqRAo0hSYRERGR/OLSIVj4MKbYCyS6F8Vt8A+4l63j6KpECjwXRxcgIiIiItlwcit82QViL2AE3MWW6q9CYA1HVyVyR1BoEhEREXF2B76BhT0hORrKNyV1yCqSPIo7uiqRO4a654mIiIg4K8OA32fB2gnW5Rr3Q8/P0Vc4kbylP3EiIiIizsiSBr+8An98al1u8hTcNx1cXMFsdmxtIncYhSYRERERZ2NOgm+HQ8gP1uVOr0GzZzRprYiDKDSJiIiIOJOESFg6AM78Dq4e8NCnULuXo6sSuaMpNImIiIg4i6unYVFviDgCnv7QbxFUaunoqkTueDkaPS8qKirb+y5dujSntYiIiIjcuc7thi86WAOTX1kY9rMCk4iTyNGdpsqVKxMZGcnly5cxDCPL/QzD4Omnn6Zfv363XaCIiIhIgXfkZ/jmUTAnQMlaMOBr8C/r6KpE5B+31D2vfPnyFCtWjMuXLxMQEEBERITtvyVKlMAwDGJjY3O7VhEREZGCZ+cXsGYsGBao0g56fwVefo6uSkSuc0uT25YoUYLz589Trlw5Lly4kO6/58+f58KFC/j56Q+7iIiISJYsFlg7EVa/YA1M9Qdb7zApMIk4nVu602T6Z7jL//5XRERERLLBnAQrn4JD31mX206AVmM0pLiIk8pWaKpfvz4mk4nY2FgaNGhAWlqavesSERERKZiuH1LcxR0enAV19Ry4iDPLVve82bNn88knn+Dj48Onn36Kq6urvesSERERKXiu/G0dIe/M79YhxQetUGASyQeydaepSZMmALi6utpeZ0bd9ERERESycGYHLOkPiZHgX976/FLJux1dlYhkwy090xQdHc2IESOIiIjI9L+GYZCYmJjbtYqIiIjkTwe+gZVPQ1oKlKkP/ZeBb0lHVyUi2ZSj0HRtbqa3334bwzCoW7cuQIb/GoahLnwiIiIihgFb34WN06zLwd2h5/+BRyHH1iUiOZKt0PTll1/i7e3Nli1bAHjiiSduesy33357e5WJiIiI5GdpZlj1POxZaF1u9gx0nAou+odlkfwmW6HJMAzmzp3Lzp07adu2LfXq1bvpMS1atLjd2kRERETyp8Qo+HoInPwVTC7Q5S1oPNzRVYnILcpWaHrsscd47LHHiIyMZMmSJcyaNYsjR47QvHlzunTpYuu2dz0NCiEiIiJ3pMiTsLgvRBwBj8LQay5U7+ToqkTkNuTomaZixYoxcuRIRo4cyYoVKxg3bhyXLl3iww8/tFd9IiIiIvnHmR3WOZgSroBvGRiwDErXcXRVInKbsjVP0/W++uordu3axcMPP8zhw4d59913M+zz6aefcvjw4Wyfc9++fXTq1AkfHx9KlSrFo48+ypUrVzLdd8uWLTRs2BAvLy9q1qzJL7/8ktO3ICIiIpL79n8NX91vDUyl68HwjQpMIgVEjkPT0qVLefbZZ3n55ZdZsWIF4eHh6bZv3LiR5557jhMnTmT7nE8//TRt2rRhx44dzJkzh19//ZUhQ4Zk2O/kyZN07dqVDh06sHPnTlq3bk2PHj04ffp0Tt+GiIiISO4wDNg0Hb4dbh1SPLg7PLoG/Eo7ujIRySW3NE9TUFAQqampfPHFFzz22GM0bNiQsWPH4u3tTc+ePZk8eTLdu3fP9vmWLl1KUFAQAHXq1CE6OprBgweTkJCAj4+Pbb+ZM2dStWpVZsyYAcBHH33EDz/8wJdffsmUKVNu5a2IiIiI3DpzEnw/Eg5+Y11u/hy0nwwuOf53aRFxYrcUmjp16sSwYcMAiI2N5f333+fBBx/EZDLx2muvMX78+Byd71pgusbLywuLxZJhv02bNtG5c2fbspubG61atWLHjh238C5EREREbkPcZevzS2f/BBc36P4+NMjYU0ZE/hWXnEp0fLKjy8ixm4ampKQkAgMDadCgAY0aNSIsLAzDMLh69Sp79uxh1apVzJ07lwceeICEhAQWLlzI0KFDKV361m5JG4bBnDlzaNKkSbq7TAAnTpygUqVK6dYFBQWxf//+LM+XnJxMcvK/v5iYmBgAzGYzZrP5lmrMLdeu7+g6Ciq1r32pfe1L7Wtfal/7uiPaN/wwbl8PxBQdhuHlT9rD8zAqtoQ8es93RBs7kNo3d4VdTWDTkQg2HbnMHycjeaBOKVp5OUf7ZrcGk5HZeOH/cfToUXbt2sUvv/zCjz/+SFxcHACdO3emRYsWPPTQQ1SrVo3U1FSGDh3K7t272blzJ4UK5Wy2a7PZzIgRI1i0aBFbtmzhnnvuSbfd1dWVefPmMXjwYNu6qVOnMn/+fI4fP57pOSdPnpxp173FixdnCGUiIiIiN1Myeg/3nPoUN0sScR6B/FHlBeK89PySyH9tvWhi20UXLiamn4qosq/Bc7XSHFRVegkJCQwYMIDo6Gj8/Pyy3C9b3fOqV6+Op6cn/fv3JykpiXfeeYfPP/+cCRMm0KhRo39P5ubGvHnzaNu2LS+88AKzZ8/OdsFnz56lb9++nDx5ks2bN2cITACenp6kpKSkW5eUlHTD8DN+/HhGjx5tW46JiaF8+fJ06tTphg2TF8xmM+vWraNjx464u7s7tJaCSO1rX2pf+1L72pfa174KbPsaBi5/forLng8wYWCp0BzPnnNp5VMsz0spsG3sJNS+OReTaGbr8Su0rh5AYU9rxDi24TgXT57A1cVEw6AitAsuQdvqJSjn78769eudon2v9UK7mWyFpiNHjtCiRQtGjhzJ+PHj+eSTT/jrr7/4v//7Pxo1akTv3r1p0KABzz//PPHx8bRt25bHH38828UePXqUtm3bUqdOHfbt20eJEiUy3a9s2bKEhYWlWxcWFkblypWzPLenpyeenp4Z1ru7uzv8l3SNM9VSEKl97Uvta19qX/tS+9pXgWrf1BT46QXYPd+63OARXLq+g4ubh0PLKlBt7ITUvjd24nIcG0PD2RASzs5TkaRaDGYPakDnWtY7rw/fE0T10v60rlYCf59/2/FalzhnaN/sXj9boemuu+5i7969vPjiixw8eBDDMHj//ffp1asXANu2baNEiRI0bdqUxo0bExsbm2FwhxsZMGAArVu3ZuHChbjcYLSZFi1asG7dOiZPngxAWloamzdv5sUXX8z2tURERERyJCESlg2G09vA5AKdXoemT4PJdPNjRQqYc1GJzN12kg2h4ZyMiE+3rWpgYdKuG8utUkAhKgXk7HEdZ5Wt0PTqq68CULlyZVauXElcXBx//PEH9evXp0mTJphMJj755BM+++wzRowYwb59+7JdwLFjx9i1axfjxo3LMLdTiRIl6N27N8OGDaNfv37873//o3HjxkydOpWePXvyySefYLFYGDp0aPbfsYiIiEh2XT4Ki/vA1ZPg4Qu9voTqnRxdlUieuRqfQnSimYr/hB+LxeCLbScBcHc10aRScdrXCKRdcCAViheMgJSZbIWma93bTCYThmGQmJhIYmIi0dHR9O7dm4SEBAASExMpVqwYy5Yto1atWtkq4MKFCwD07t07w7YPPviAw4cPc/78eQDq16/PkiVLGDduHNOnT6dx48asXbsWX1/fbF1LREREJNuOrYNvhkFyDBSpAAOWQWANR1clYleGYXAsPI4NIeFsDL3ErtNXaRdcki8esY43UL6YD0+3qUKdsv60qBaAr9ed0X0xW6HplVde4dSpU7zzzjtMmzaNWbNmUa5cORo0aEBSUhKrV6/mmWeeYd26dbaHup577jkCAgJueu5WrVpxowH8nnvuuXTLvXr1snULFBEREcl1hgG/fwzrJoJhgaBm0HchFLr59xqR/Oq34xGsO3yJDaGXCItMTLctMj4ZwzAw/dMl9aXOwY4o0aGyNV31/v37qV+/Ph4e/z7s+Morr/Dqq68yatQo/P398ff3p1u3btStW5cHH3yQZcuW2a1oEREREbtITYbvR8LaV6yBqcEQGPKDApMUONGJ6ecn+nD9MeZtP0VYZCIebi60uasE0x6qxW/j2vHtiOa2wHSnytadpjp16nD06FHbqHbNmzfn8OHDlCtXjsTERJo1a8a+fftYtWoVAD169GDXrl32q1pEREQkt8WFw7JBEPaHdcCH+96AJk9qwAcpEAzD4PCFGDaGhLMhNJyD56L585UOFCtkvSnSo0FZKpcoRLvgQFpUC8DHI1sx4Y6R7da4fhjwp556itGjR1OuXDm8vb359ttv082V1LVrV7p27Zq7lYqIiIjYy4V9sGQAxJwFL3/oPQ+qtHN0VSK3Jcmcxva/I/55PimcC9FJ6bbvOn2VjneXBKB/4yD6N87+6Nd3mmyHpv8O671ixQrq1KmT6wWJiIiI5KlDK2Hl02BOgOLVoP9SCKjq6KpEbsn1zx79sPc8L67Yb9vm5e5Ci6olbKPdlfTzclSZ+U62Q9OsWbOYMGEChmEwffp0xo0bZ/uF9OvXj5SUFBo0aACAj48PI0aMYMCAAfapWkREROR2WSyw+Q3Y8pZ1uUp765Di3kUcWpZITlgsBgfORbMh1DraXc/65RjWohIAbYJLULaIN22DS9A+uCTNqhTHy93VwRXnT9kOTZ6enrz88ssAvPvuuxQrVsw26t3IkSP57rvvmDZtGgDr169n5MiRCk0iIiLinJJi4Lsn4cga63LTkdBxKrjqOQ5xfgkpqWw79k+3uyPhXI5Ntm3z975kC02Bvl5se6ntHT+IQ27I9t8MN2rsli1b4urqSrdu3QBo2LAhH330UbrbgyIiIiJO4crfsHQAXA4FV0+4/0Oo19/RVYlkS0qqhSbTNxCblGpbV8jDlVbVS9AuOJC2wYHp9td38dyR7dB0o7mU/is5OVmBSURERJzP8Q3wzaOQFA2+paHvIijX0NFViWSQZjHYG3aVDSHhnIlMYNYA62MwHm4uNKxQlL8vx9E+uCQdapSkcaVieLhlayYhuUV2uQddvHhx/vjjD3ucWkRERCTnDAN2fAJrJ1jnXyrXyDphrW8pR1cmYhObZGbL0Qg2hF5i85HLRMan2La93DWRMkW8AZg1oAGFPFx1gyIP5Xpo2rFjB1FRUXTu3Dm3Ty0iIiKSc+YkWDUK9i22LtcbCN3eA3eNHCbO45PNx3lv7VFSLf/27vLzcqPNXYG0rxGIv7e7bX1hTz17l9dytcWPHj1Kt27dePXVVxWaRERExPGiz1onrD2/B0yucN90TVgrDpWaZuGv01fZGBpO74blqFbSF4DyRX1ItRhULlGI9sGBtK9RkoYViuLuqm53zuCWB4KIj49Pt84wDEaOHMkrr7zCc889l3sVioiIiNyKU9vg60cgIQK8i0HvuVC5jaOrkjtQVEIKvx69zIaQcDYfCSfmn0Ec/LzcbKGpXXAgm8a0oVJAIUeWKlnIdmiKiYmhevXqtteVK1fm/vvvt203mUz88MMPeHt7536VIiIiItllGPDn/8EvL4MlFUrVtg74ULSCoyuTO8z5qESeX7aXXaevknZdt7uiPu60vSuQ+kFFbesKebpRSd3unFa2fzP79u1Lt+zt7U3lypVty4ZhKDCJiIiIY/33+aVaveCBmeDh49i6pMBLSbXw58lI4lNSua+mdYCRgMKeHDoXTZrF4K6SvrSrEUiHGoHUK18UVxd1Ec1Psh2aatasecPtrVq1uu1iRERERG5ZuueXXKyT1TZ7Rs8vid1ExCWz+chlNoZeYsvRCOKSU6kUUMgWmjzcXJg1oAFVAwtTvpiCe36Wa/cAf/nll9w6lYiIiEjOnNoGy4dC/GXwLgq95kKVto6uSgqohTtO8+3us+wJi+L6qUwDCnvSuGIxksxpeLm7AmSYbFbyJ3WcFBERkfzLNv/SRDDSoGRt6LcQilZ0dGVSQCSZ0/jjZCQtqgbYutQdOh/D7jNRANQs40f7GiVpHxxI7bL+uKjbXYGk0CQiIiL5U0o8/PAsHFxhXa7dB+7/UM8vyW0Lj03m90smfly0h9/+jiTRnMaKp++lYQXrwA197ilHrbJ+tAsOpLS/num/Eyg0iYiISP5z5W/r80vhh8HFzTr/UuMn9PyS3LJzUYks/yuMjaHh7D8bDbgClwEo5edFRFyybd/6QUXTjXwnBZ9Ck4iIiOQvR3+BFcMhORoKl4TeX0GFZo6uSvKZxJQ04pJTKeHrCcDF6CQ+WH/Mtr1CYYOHGlelY83S1Czjl2HOUrmzKDSJiIhI/mCxwJa3YPMb1uXyTayBya+0Y+uSfON8VCIbQsPZGHKJ7X9foWeDcrzRszYA9coXoWf9sjStUpwWlYuyc+sGuratgru7u4OrFmeg0CQiIiLOLyESvn0Cjq+zLjd6HO57A9w8HFuXODXDMNgbFsXG0HDWh4QTciEm3fajl2Jtr11dTLzXtx4AZrM5L8uUfEChSURERJzb+b3w9WCIOgNuXtD9fag3wNFViZNKSbXg4eYCgMlkYvTX+zgZEQ+AiwkaBBWlXY1A2geXpHrJwo4sVfIRhSYRERFxXrvnw+oxkJZsHUa8zwIoXcfRVYmTCYtMYEPIJTaEhnPwXDR/vNzBFpzur1uGvy/H0T44kDZ3BVKskO5OSs4pNImIiIjzMSfBmjGwZ4F1uXpn6DHbOnGt3PFS0yzsCYtiQ0g4G0IucSw8Lt32Xaev0qxKcQBGd6zuiBKlgFFoEhEREedy9RR8PQQu7ANM0O4VaPECuLg4ujJxEl9sO8mbP4Xall1dTDSqWJR2wYG0r1GSygGFHFidFEQKTSIiIuI8jq6Fb4dDUhR4F4Nec6BKO0dXJQ5y4nLcP4M4XGJIs4p0rW0dKbF19RJ8uvlv2t5VgnY1StK6egn8vTXKndiPQpOIiIg4XloqbJ4OW9+1LpdpAH3mQ5Hyjq1L8pQ5zcLOU5FsDAlnQ2i4bQAHsE4wey00BZfyZdeEDri56u6j5A2FJhEREXGsuHD4Zhic2mpdbjQc7nsd3DwdW5fkqehEMy1nbCQmKdW2zt3VRJNKxWn/z2h315hMJtxcNdms5B2FJhEREXGcU79ZA1PcRXAvBA98BLV7OboqsSPDMDgWHseGkHCiElIY37UGAP7e7pQr6sPFmCTa3hVIhxqBtKgWgK+Xut2J4yk0iYiISN4zDPjtQ9gwFYw0KBFs7Y5X4i5HVyZ2kJyaxh8nItkYGs6G0EuERSYC4OHqwv/aV6OQp/Ur6dxHGxFQ2BNXF91FEuei0CQiIiJ5K/EqrBwBR9ZYl+v0tU5Y66ERzwqiD9cf47Mtf5OQkmZb5+Hmwr1VitO+Rsl0+5b088rr8kSyRaFJRERE8s65XbB8KESdAVcP6PIWNBwKJt1ZyO8Mw+DwhRg2hoTTt3F5An2tAaiwlxsJKWkE+nrSvkYg7YJL0rxqcXw89DVU8g99WkVERMT+DAP++AzWTgCLGYpUgD5fQZn6jq5MbkOSOY3tf0ewISScjaHhXIhOAiDQz5O+jYIAeLBeGRpXLEbNMn64qNud5FMKTSIiImJfiVHwwzMQ8qN1ucb98MAs8C7iyKrkNpyKiOe11YfZdjyCJLPFtt7L3YUWVUtQpoi3bV1AYU8CCmskRMnfFJpERETEfs7vsXbHu3oKXNyh02vQ5El1x8tHLBaDA+eiSUmz0KhiMQD8vN3ZGBqOxYAy/l60qxFI+xolaVa5OF7urg6uWCT3KTSJiIhI7jMMXP6aA+snQloKFAmCXvOgXENHVybZEJ+cyrbjEWwMCWfjkXAuxybTuGIxvn6qGQDFCnnw5sN1qFXGnxqlfTEpBEsBp9AkIiIiuSspmntOzcJ1707r8l3d4KGPwbuoY+uSm/p6ZxirD1zg9xNXSEn9t9tdYU83Av08sVgM23NJfe4p76gyRfKcQpOIiIjknnO7cFv+KGWjTmO4uGHqOBWajlB3PCeUZjE4fD6G2uX8bevWhVzi16OXAShfzJv2wSVpXyOQJpWK4+Hm4qhSRRxOoUlERERun2HA7x/D+smYLGbiPQLwHLAYt4pNHF2ZXCc2ycyWoxFsCL3E5iOXiYxPYcvYtgQV9wGgf+Py3FOhKO1rBFKlRGF1uxP5h0KTiIiI3J74K7DyaTj2CwCW4AfY7N6FTmUbOLgwAbgYncTqAxfYGHqJP05EkmoxbNt8vdz4OyLOFpraBZekXXDJrE4lcsdyqvusBw4coGHDhmzbti3LfSpUqIDJZEr3ExERkYdVioiIiM3p7TC7hTUwuXpCt3dJ6zmHVLdCjq7sjpWaZiEuOdW2vDcsimmrDvPb8SukWgwqlyjE8JaVWPpEU3ZP7EjbuwIdWK1I/uAUd5p2797NjBkz+PHHH0lMTLzhvleuXGHRokU0btzYtq5YsWL2LlFERESuZ0mDre/B5ulgWKB4Veg9D0rVBrPZ0dXdcaISUvj16GU2hISz+Ug4Q5tXYnTH6gC0qBZAy2oBtK5egvY1SlIpQIFWJKecIjR9++23eHh4sGrVKtq3b5/lfikpKcTHx1O7dm2qVq2ahxWKiIiITcx5+PYJOLXVuly3P3R9BzwLO7auO4hhGFxMgM+3nWTz0SvsOn2VtOu63f11KtL2urCnGwse07NlIrfDKULTtGnTMJlMnDp16ob7RUZa/wIICAjI9rmTk5NJTk62LcfExABgNpsxO/hfwq5d39F1FFRqX/tS+9qX2te+1L63znT0J1xX/Q9T4lUM90KkdX4Lo05f68b/tKvaN3cZhmEbmCEpJYUPDrqSuO+YbXv1wMK0vasE7YJLULecv9r/NugzbF/O1L7ZrcFkGIZx893yxqlTp6hUqRJbt26lRYsWGbYfOnSIWrVq4enpSfHixWnYsCGvvfYaderUyfKckydPZsqUKRnWL168GB8fn1ytX0REpKBysaRQ8/wyKl9eB0CUd0X+qjiCeK9SDq6sYIs1Q8hVEwevmghPMvFSnTTb6O2LjrsQkwI1ixrULGpQ3MuxtYrkRwkJCQwYMIDo6Gj8/Pyy3C9fhabY2FgOHz6Mj48Pp06d4s033+Tw4cMcOHCAcuXKZXrOzO40lS9fnoiIiBs2TF4wm82sW7eOjh074u7u7tBaCiK1r32pfe1L7Wtfat8cijiG23fDMYUfBCCtydNY2kwAN89Md1f73jrDMDh6KY6NRy6z6chl9p6N5vpvaqufaUb1kr6YzWbWrl1Hp05qY3vQZ9i+nKl9Y2JiCAgIuGlocoruednl6+tLkybWPrm1a9emdevWVKhQgSVLljB27NhMj/H09MTTM+Nf6u7u7g7/JV3jTLUURGpf+1L72pfa177UvjdhGLBnIfz0IpgTwCcAHvoU1+qdcM3G4WrfnHv7l1A+3vR3unU1y/jRPjiQ9jVKUqOMPy4u1ltNJpPa2N7UvvblDO2b3evnq9D0X35+flStWpXTp087uhQREZGCJfEq/PgcHP7eulypNfT8P/BVd7zcEB6TxMbQcDaEhvNEq8o0qmgdCbhJpeJ8sfUkLaoG0L5GSdoGl6C0v7eDqxWRfB2aoqKiOHr0KAMHDnR0KSIiIgXHqW3w7ZMQcxZc3KDtK9D8eXBxqukd8xXDMDh4LoYNoZfYGBrO/rPRtm0Vi/vYQlOzKsXZ+2onvD2ycy9PRPKK04em/v3706hRI0aPHs3q1as5cuQIbdq04erVq0yePBlfX18eeeQRR5cpIiKS/6WZYfMb1vmXMKBYZXj4Cyjb0NGV5WvnoxLp8clvXIpJTre+bvkitA8OpHOtf+/eubu64K68JOJ0nD40hYSEEBhonam6SJEifP7557zyyisUL16cNm3asGzZMooWLergKkVERPK5yBOw4nE4t8u6XH8QdJ6huZdy6FxUIhtDwzGnWhjWohIApfy8MAzw8XClZbUA2geXpE1wCQJ9NdydSH7hVKGpYsWK/Hcwv71799peN2/enJCQkDyuSkREpAAzDNi3FNaMgZQ48PSH+z+AWj0dXVm+YLEY7D0bxcYQ6/NJIRes80EWL+TBI/dWxNXFhIuLiUWPNyGouA+ebrqNJJIfOVVoEhERkTyUEAmrR8Oh76zLQfdaB3soUt6xdeUTH6w/ysIdp4mIS7GtczFBg6CitK9REnOaBVcXa0iqVtLXUWWKSC5QaBIREbkTndgM3z0Nseetgz20GQctRoOL7oRk5syVBDaGXqJf4yC8/nnoKMlsISIuBV9PN1rdVYIONQJpXT2QYoU8HFytiOQ2hSYREZE7SWoybJgKv8+yLhevar27pMEe0klNs7D7TJR1tLuQcI6FxwEQVNyHdsElAejXqDytqgXQqFIx3F01sqBIQabQJCIicqe4dNg62EP4IevyPcOg02vgUcixdTmR4+GxzNp4nM1HLxOVYLatd3Ux0ahiUTxc/70TVzGgEBUD1HYidwKFJhERkYLOYoE/P4N1kyAtGXwC4MFZcFcXR1fmcH9fjiPNYlDd9syRiZV7zwPg7+1O27tK0K5GSVpXL4G/t7vjChURh1JoEhERKciiz8LKEXDyV+tytfusgalwoGPrchBzmoWdJyPZEBrOxtBwTkbE0612aT4e2ACAKiUKMfa+u2hUsRgNgorgpm53IoJCk4iISMFkGLD/a1gzFpKjwd0HOk2Dex4Dk8nR1eW5lXvOsS7kEluOXCY2OdW23t3VhOW66U5MJhMj21Z1RIki4sQUmkRERAqahEhYNQoOr7Qul20IPf4PAu6MMGAYBmevJlK+mI9t3dztp9gXFgVY51BqGxxIhxqBtKhWgsKe+jokIjemvyVEREQKkmPr4fuREHfROpR465esQ4m7Fuz/5SenpvHHiUg2hoazIfQSF6KS2P1qR/y8rM8hDWwcRIuqxWlfoyT1yhXBxeXOu9smIreuYP8NKiIicqdIjoN1r8Jfc6zLAdWhx2dQtoFj67KjiLhkNoZYQ9LWYxEkpKTZtnm4uRByPoYmlYsD0KeRJuwVkVun0CQiIpLfnf4dVj4NV09al5s8BR0mg7u3Q8vKbYZhkGoxbHMi/XTgAhO/P2TbHujrSbvgQNrXKEnzqsXx8dDXHBHJHfrbREREJL8yJ8Gm12D7LMAAv3LWkfGqtHV0ZbkmyZzG9r8jWB8SzsaQcEa2q8rgphUAaFejJF//dZb2NQLpUKMkNcv4YboDB7kQEftTaBIREcmPzu+B756Cy6HW5XqDoPN08PJ3bF254GJ0kvXZpJBL/PZ3BElmi23blqOXbaGpbBFvfny2haPKFJE7iEKTiIhIfpJmhi3vwJa3wUiDQoFw/4cQ3NXRleWK+ORUWr61EXPav8OAl/H3on2NkrSrEUizf55REhHJSwpNIiIi+cWlw7DyKbiwz7p890PQ7T0olP+CRHxyKluPRbAx9BKR8Wa+eOQeAAp5utG4UjESU9KsQSk4kOBSvup2JyIOpdAkIiLi7NJS4bf3YfMMsJjBuyh0exdqPezoynIkLDLhnyHBw9nx9xVS0qzd7kwmuBybTAlfTwDmPdrYNtiDiIgzUGgSERFxZuEh1pHxzu+xLlfvAvd/AL6lHFpWTk1bdZg5206mWxdUzIf2NQJpH1ySIj7utvUKTCLibBSaREREnFFaKmz/EDa/CWkp1gEeurwFdfpab804qZgkM5tDLrLwmAs1IuKpXroIAHeX9sPVxUTDCkVpHxxI+xqBVClRWN3uRCRfUGgSERFxNuGh/9xd2m1drt4Zun8AfqUdWlZWTkXEsz7kEhtDw/nzZCSpFgNwYeORy7bQ1KV2KdrXCKSIj4dDaxURuRUKTSIiIs4izQzbP0p/d6nzDKjbzynvLh0Pj+OJBX9x4nJ8uvWVAwpR0T2WppWK2db5eLihvCQi+ZVCk4iIiDO4eAC+H/nvyHjVOlmHEvcr49i6/hGVkMLmI5dxdTFxf11rTeWKenM+KhE3FxNNKhejXXBJ2gcHUtbfgzVr1lCzjJ+DqxYRyR0KTSIiIo6UmgJb34Gt74IlFbyKQJcZDn92yTAM/r4cx/qQcDaGhPPX6UgsBtxV0tcWmrzcXZk/rAnBpX3x8/p3IAez2eyoskVE7EKhSURExFHO7bbeXQo/bF0O7m6dd8m3pEPL+nD9MVbsPsuZyIR064NL+dIuOJA0i4GrizXQNb6uC56ISEGl0CQiIpLXzInW55a2fwSGBXwCoOvbULNHnt9diohLZtuxCB6sV8Y2kt2ZyATORCbg4epCsyrFaRccSLvgQMoX88nT2kREnIVCk4iISF469Rv88CxE/m1drtXL2h2vUECeXN4wDEIvxrIh5BIbQsPZGxaFYUDVwMLUKusPwJBmFehUsyQtqgZQyFNfFURE9DehiIhIXkiKhnWTYNdc63LhUtD9PQjulieXP3Yplq9+P8XGkHDORyel21arrB+xSam25brli1A3T6oSEckfFJpERETsLXQNrH4BYs9blxsOhQ5TwLuI3S55KSYJi2FQ2t8bgMtxySzccQYAL3cXWlQNoF1wSdoFB1LK38tudYiIFAQKTSIiIvYSFw4/vQiHvrMuF6sM938ElVrm+qUsFoND52Nsk8weOBfN0HsrMvmBmgA0qliMofdWpFX1AO6tEoCXu2uu1yAiUlApNImIiOQ2w4B9S+Dn8ZAUBSZXuPdZaDMO3L1z7TIWi8GG0HA2/BOUwmOTbdtMJrh83bK7q4stQImISM4oNImIiOSmK3/Dqufh5Bbrcqk68MBMKFMvV04fnWjG39s6J5LJBJN/OMS5qEQACnm40qJaAO1rlKTtXYGU8PXMlWuKiNzpFJpERERyQ2qKdQjxX9+CtGRw87beWWo2Elzdb358FtIsBvvORllHuwsJ52JMEn+90gE3VxdMJhN9G5UnMj6FdsGBNKlcDE83dbsTEcltCk0iIiK3K+xP+PG5fyeprdLOOkltsUq3dLrYJDPbjkWwPiSczUfCuRKfYtvmYoLQi7G24cH/177abZcvIiI3ptAkIiJyq5KiYcNU2DkHMKyT1HZ+A2r3zvEktYZh2CaX/XzLCT7aeNy2zdfLjdbVS9C+RiBtqgdStJBHbr4LERG5CYUmERGRnDIMOLwSfhoHcRet6+oNgk7TwKdYtk6RmmZh95koNoRau92Nve8u7qtZCoD2NUry4/4LtA8OpF2NQBpVLIa7q4ud3oyIiNyMQpOIiEhOXD0Fq8fA8XXW5WKVofsHULn1TQ+NTjSz5ehlNoRcYvPRy0QlmG3bNoRcsoWmOuX82TSmTe7XLiIit0ShSUREJDtSU+D3WdaBHlITwdUDWoyGFqPA/eaTw4bHJNHszY2kWQzbuiI+7rS9K5B2wYG0ql7Ctt6Uw659IiJiXwpNIiIiN3P6d1g1Ci6HWJcrtoTu70NAxkEYUlIt/HUqkvUh4VgMwzY3UqCfF5UCCmEC2tUIpH1wSRoEFcFN3e5ERJyeQpOIiEhW4q/A+kmwZ4F12ScA7nsd6vRNN9BDZHwKm4+EsyEknC1HLxObnAqAt7sr47oE4+VuHQb8uxH34ut168OPi4iIYyg0iYiI/JfFYg1K6ydB4lXrugaPQIfJGQZ6mLjyIAv/OI3xb687Agp72LrduVwXrhSYRETyJ4UmERGR613YB6tfgLM7rcsla0G390gucw87TkSyMeQgz3eobhv2u0wRbwwDapT2o0MNa1CqW64ILi56LklEpKBwqtB04MABhg4dyocffkiLFi0y3efgwYOMGDGCnTt3Urp0aaZOncqgQYPyuFIRESlwkqJh03T48//AsIBHYWLvfZGfvR9g/a9X2HpsHQkpaQDUDyrKQ/XLAtDnnnI8WK8MZYp4O7J6ERGxI6cITbt372bGjBn8+OOPJCYmZrlfdHQ0HTt2pFOnTsyaNYsffviBRx55hKpVq9K0adM8rFhERAoMw4ADy2HtBIi7BEB05ft5Pqo3m352Aw7bdg309aR9jUAqBRSyrSte2DOvKxYRkTzmFKHp22+/xcPDg1WrVtG+ffss9/vqq6+wWCx8/vnneHh4UKdOHVatWsWnn36q0CQiIjkXfhjLL+NwObPduly8KnR9h+QSzdg0fQNgnTOp7V2BdKhRkppl/NTtTkTkDuQUoWnatGmYTCZOnTp1w/02bdpE27Zt8fDwsK1r164dK1assHOFIiJSkFy6HE6xo4tw2bMOFywkGh6s8u9P76ffBjdPAoFPBzagQYWilPS7+RxMIiJSsDlFaMruJH4nTpyga9eu6dYFBQVx7ty5LI9JTk4mOTnZthwTEwOA2WzGbDZndVieuHZ9R9dRUKl97Uvta19qX/v4ZNNxUvcuZUj8l7Q0Wf9/sCatMZ97D6NulVo8aDFh+qfNOwQHAPod3Ap9fu1PbWxfal/7cqb2zW4NThGasisuLg4fH59063x8fEhKSsrymDfeeIMpU6ZkWL927doM53KUdevWObqEAk3ta19qX/tS+9665DQ4FWviriLWscD9Ek7T4eh8ahrHwARnKM33/oNxK1mLR3zAxAl++umEg6suWPT5tT+1sX2pfe3LGdo3ISEhW/vlq9Dk6elJSkpKunVJSUk3DD/jx49n9OjRtuWYmBjKly9Pp06d8PPzs1ut2WE2m1m3bh0dO3bE3V1zd+Q2ta99qX3tS+17a85FJbLpyGU2hl5mx8lIzGkGvz1Ti1K738Pl6HxMhgWzqzfxjZ9nb0I1Hruvi9rXDvT5tT+1sX2pfe3Lmdr3Wi+0m8lXoals2bKEhYWlWxcWFkblypWzPMbT0xNPz4wjG7m7uzv8l3SNM9VSEKl97Uvta19q35s7Hh7Lit3n2BgSzpFLsbb1rqTxvO8WSs5/CteUf/6nWLMn7p1eo5BPIMaaNWpfO1P72p/a2L7UvvblDO2b3evnq9DUokUL5syZQ1paGq6urgBs2LDhhiPuiYhIwRKTZMawgL+P9X90hy/E8unmvwFwMcE9FYoxuNQpOp15H8/II9aDStaGLjOgYnPrshP0oxcRkfzD6UNT//79adSoEaNHj2b48OG8++67PPPMM4wcOZLvvvuOAwcOsGTJEkeXKSIidnQqIp4NoeFsCLnEnycjGdWxOiPbVgWgdbUSPFivDO2CA2lbMhG/LVNg7w/WA72LQruJ0HAouLg67g2IiEi+5vShKSQkhMDAQADKlCnDjz/+yDPPPMOXX35JzZo1WbNmDRUqVHBwlSIikpvSLAY7T0WyIeQSG0LDOXE5Pt32Ixf/7Ybn7+POhz2qwW8fwKqZkJoEJhdo9Di0GQ8+xfK4ehERKWicKjRVrFgRwzDSrdu7d2+65datW3PgwIE8rEpERPKCOc2Cu6sLAKkWC4/N20l8ShoAbi4mmlQuRrvgkrQLDqRSQCHrQRYL7F8K66dA3EXruootrV3xStZ0xNsQEZECyKlCk4iI3DkMw+B4eBwbQsPZGBLO1YQU1o1uDYCnmysP1CtDcqqF9sElaVk9AD+v/zyse2YH/DwOzu+xLhetCJ1eg+DukM35/0RERLJDoUlERPJMcmoaf56MZENIOBtDwzkTmX5+jLDIBMoXs04j8UbPOpmfJCoM1k+Cgyusyx6+0GoMNH0a3DKOlioiInK7FJpERCTPTFt1mIU7ztiWPVxdaFalOO1rBNL2rkBbYMpUcixs+wB+n2V9bgkT1B9kHejBt6TdaxcRkTuXQpOIiOQqwzAIuRDLxlDrIA6vdr+b+kFFAWhdPZBfDl2i3V2BtKsRSIuqARTyvMn/itJS+f/27jw+6ure//hrJstkskKWCRCWJARIRBZBARFZElAv7l7LVevDpV57tWpbvd5W26tW/Wmvl9b2qpeq9apdrPdqba0VRSEsghoQkEVIWAOExWxkJSSZzJzfH18YGBKSgJnMJHk/H495TOZ8Tyaf7ydnJvPJ93zPly//AMuehiNlVtuwi+Cyn8PAcQHeGxERERVNIiLSBRrdHj7fXUl+YSlLC8s4WNPo27aksNRXNOVmu1j9cB52eyfPOdq5BD5+BMq2Wo8TM2HOEzpvSUREupWKJhER+UZ2ltVx5fOfctTt8bVFRdiZlpXMrGwXs3NOTJ0L62yxVLoVPv532JV/7An7wYwfW8uIh0d2YfQiIiIdU9EkIiKd4vUavjpYQ35hGc7IMO6aMRyAjORYHBF2+kVHkJvtIi/HxdThyURFnMXFZOu+tqbhffkHMF6wR8Ck71oLPeh6SyIiEiQqmkRE5LQamlv4dOexaXdFZZTVNQEwMCGKf5meic1mI8xu44PvX8zAhChsZztlrqkOPnveurmPraiXcyXMfhyShnfR3oiIiJwdFU0iItKmn/51M2+v209zi9fXFh0ZxsUjksnLSaXFa4gIs4qkQf2cZ/dDPG5Y/ztY/h9wpNxqGzwJLnkShk75prsgIiLSJVQ0iYj0cR6vYeP+apYXlXFv7ggiw+2AdYHZ5hYvg/s7yct2kZeTyuTMRBzhZzHt7lTGQNFCWPIzqNxhtSVmwuyfQc5VWuRBRERCioomEZE+qK7RzaodFeQXlbGsqIzKI80ATM5M4qKsZABuvyidGyYNYYQr9uyn3bVlXwEsfgxKCqzH0ckw8yGYeBuERXTdzxEREekiKppERPqQDSXV/OKjbawursTtMb72uKhwZoxMIfakaya1e6HZs1G6FfKfgO0fWo/DnXDhPXDRDyAqvmt/loiISBdS0SQi0ku1eLys21tFbFQ4owclABARZmPVzgoAMpJjyMu2LjJ7QXoiEWH2wARSvQ+W/Rw2vgkYsIXBhFusJcTjBwbmZ4qIiHQhFU0iIr1ITYObFTvKyS8sZfm2cmqOurn2vDR+9U/jAThnYDxPXD2aaVnJZKbEBjaYI5Ww8pfwxW/BY03/45yrIfcRSB4R2J8tIiLShVQ0iYj0cF6v4X9WFbOksJS1e6vweE9Mu+sXHUGC88R5QjabjVsuTA9sQI21ULAAPnsBmuustvSLYc7jkDYxsD9bREQkAFQ0iYj0MM0tXnaU1fmm3NntNt5Zv5+ir60CZYQrlrycVPJyXEwY2p8wezetROc+Cl+8AiufhaOHrbYBY2H2YzA8TyviiYhIj6WiSUSkBzh8pJnl28rILyzjk+3lNHm8bHh0DtGR1tv4nRdnUtfoJjc7laFJXbyAQ0c8bvjyD7DiP6HukNWWNAJyfwo5V4M9QOdKiYiIdBMVTSIiIar8KLy4YjfLd1Syfl8V5sSsO5JiItldfoRz06yjTf84cXD3B+j1wOY/w/KfQ1Wx1ZYwxFo+fOwNEKY/MSIi0jvoL5qISIhodHsAiIqwLh77VZWNdzfs9G0/Z2A8eTkuZmW7GD+4H/bumnZ3Kq8Xtr4Ly/8DKrZZbTEpcPGDcP7tEO4ITlwiIiIBoqJJRCSIyuoaWV5UzpLCUlbtrOBnV41m3vlDADi3v6HakczscwaQm+1iUD9ncIM1BooWWkeWSr+y2qL6wdT7YPJd4AjwanwiIiJBoqJJRKQbGWPYcrCWpUVl5BeVsbGk2m/7F8WHfUVTihN++48TiIiIaOOZupExsGMxLHsKDm2w2hzxMOV7cOH3ICohqOGJiIgEmoomEZEAM8ZgO7ZyXFWDmytfWOV3ftK4wQnkZlur3Y0eFB+kKNtgDOxaak3D27/GaouIgcn/Yh1dik4MbnwiIiLdREWTiEgAHKo5ytKiMpYWluExhtdvnwRAYkwk07KScUaEkZvtIjfbhSs+KsjRnqKtYik8Ci74Z5h2P8QkBzc+ERGRbqaiSUSkC3i9hk0HalhaWMqSwjK2Hqr1bQuz26hpcJMQbU2z+/13JvmOPIWU0xVL598BF30f4gYENz4REZEgUdEkItIFHnhrA+9uOOh7bLPBhKH9yc12kZfjIt4ZftK2ECuYjIFd+bD8mTaKpR9AXGpw4xMREQkyFU0iImeg5HCDbxGHp645lyGJ1oVkJ2UksaSwjBkjU8jNdjFzVApJsSG+9LYxsH0RfDIfDqyz2lQsiYiItKKiSUSkHR6v4ct9VeQXlZFfWMr20nrftqVFZdw6NR2A6yakcf3EwUSG24MU6RnweqHo71ax9PVmqy3caV1j6aIfqlgSERE5hYomEZHT2FhSzW2vraGqwe1rC7PbOH9Yf/JyrEUcjjt+QdqQ5vXAV3+Blb+A8iKrLTLWWuDhwnshNiW48YmIiIQoFU0iIkBxxRHyC0tJjInkugmDAchMiaG+qYX4qHBmjrLOTZoxMoV+0ZFBjvYMtTTDpv+DVb+Cw7usNkeCtXT4lLu1dLiIiEgHVDSJSJ/k9nhZu6eKpUWl5BeVsbv8CABjByf4iqa4qAj+ds80RqbGEh7WA6bdnar5CKz/PXz2PNQesNqc/WHKPTDpTnD2C2p4IiIiPYWKJhHpc3761838feNBahtbfG3hdhuTMxOZnZPqdzHac0LpYrOddbQavvgtFPwGGiqtttgBMPVemHgbOOKCGZ2IiEiPo6JJRHotYww7y+r5bFclt1w4zFcI1Ta2UNvYQmJMJLOOTbubNiKZ+KiIIEf8DdWVwurfwJpXoLnOauufbq2EN+4miAixi+iKiIj0ECqaRKRXaW7xsrq4kvzCMpYWlbHvcAMAU4cnMSLVOsLyL9MzuW1qOuOH9CPMHmLXTDoblbvgs+dgw5vgabLaXOfAtAdg9LUQprd6ERGRb0J/SUWkV1i/r4rffrKblTsqqG86Me0uMszOhcOTaGrx+trOTUsIRohd78A6WPVrKPw7YKy2wZNg2v0w8jKw98DzsEREREKQiiYR6XGMMRQeqiMuKtx3cdnao24+/OprAFLiHOQem3Z3UVYyMY5e9FZnDOzMh09/DXtWnmgfeZl1jaVhFwYrMhERkV6rF32SEJHerNHt4fNdleQXlbK0sIyDNY18d3omP5mbA8CUzCR+kDeC3GwXY9ISsPeGaXcna2mCzX+Gz/8byrZYbfZwGDMPpt4HqecENz4REZFeTEWTiISs5hYv76zfT35hGZ/urOCo2+PbFhVhp/mkKXdREWHcP2dkMMIMrKPVUPAHWP0S1FtH0oiIsVbBu/B7kDA4mNGJiIj0CSqaRCRkeL2GQ7WNpPVzAtYy4L/8eDsV9dbiBgMTosjLcZGb7WLq8GSiIsKCGW5gVe/l3P1/JPz5u8FtXUOKuIEw+S6rYNI1lkRERLqNiiYRCaqG5hZW7ahgaZG12p3XwJqf5GG327DbbXxnWjoejyEvJ5WcgXG+ZcN7JWOgZDUULCC88O8MN8eOpKWeCxfeC+f+I4RHBjdGERGRPkhFk4h0u4PVR8kvLCW/qIzPdlX6TbOLiQxj7+EGMpJjAPjezKxghdl9PG7Y8i4ULICD6wGwAaVxY0i64jHCR86G3lwsioiIhDgVTSIScB6vtRz28Wsi/e7zPby0Yrdv++D+TmbnpJKb7WJyZiKO8F487e5kDYdh3euw5rdQd9BqC3PA2Hm4z/8uBWuLmZs5UwWTiIhIkIVE0WSM4YknnuCll16ipqaGSy+9lJdffpnk5GS/fh6Ph4iICIwxvraYmBjq6+u7O2QR6UBdo5uVOyrILyxj+bYyfjFvHLNGuQCYk5PK+r1V5GanMjvHRZYrtndPuztV6VZY8xJs/D9oOWq1xbhg0p1w/ncgJhncbqA4qGGKiIiIJSSKpvnz5/Pcc8/x+uuvk5SUxB133MGtt97KwoUL/fpVVVVhjGH58uWkpaUBYNfFG0VCxr7KBpYUlrK0qIzVxZW4PSf+wbFiW7mvaDo/PZG375oarDCDw+uBbR/C6hf9r680YAxMuQfOvQ7CHcGLT0RERE4r6EWT1+tl/vz5PPLII1x55ZUAPPvss8ydO5fi4mIyMjJ8fQ8fPgzAhAkTiIuLC0q8ItK23eX15P5yhV9bZnIMudku8nJSOT+9f5AiC7KGw/DlH2DNK1Czz2qzhUH25TD5X2DYRZp+JyIiEuKCXjRt3ryZiooKLrvsMl/bzJkzsdvtFBQUtCqaIiMjz6hgampqoqmpyfe4trYWALfbjdvt7oI9OHvHf36w4+itlN/AqDl6bNpdURlVZXbmHMvv4IRIMpKiSY13MGtUCrNGpfgWcwDA68Ht9ZzmWXuhrzcRtu5VbF+9g+3YFDzjTMR73i14J94O8dbRclpa2vx2jd/AUn4DS/kNPOU4sJTfwAql/HY2Bps5+QShIPjrX//KddddR2NjIw7HiakpAwYM4MEHH+TBBx/0tS1cuJArrriCqKgoXC4XF110EU8//TTp6emnff6f/exnPP74463a//SnPxEdHd2l+yLSGxkDZY2wpcrGlio7u2vBi3VkxBlmeOp8D2HHZsl6vPi+7ovs3mYGVX9BRvkSEht2+dqrnUMpTrmE/f2n4LVryXAREZFQ0dDQwE033URNTQ3x8fGn7Rf0I0319fXY7Xa/ggkgOjqaxsZGv7bJkyezZs0aHA4HRUVFPP7448yaNYtNmzad9ujTww8/zAMPPOB7XFtby5AhQ7jkkkvaTUx3cLvdLF68mDlz5hARERHUWHoj5bdr3PPmBj7eWubXNsIVw4ysJKJrdjNnzmyiHH28EKjei33977BvfANbQyUAxh6BybkS74TbiRkyhXNtNs49g6fU+A0s5TewlN/AU44DS/kNrFDK7/FZaB0JetHkcDjwer20tLQQHn4inMbGxlZHgpKTk30r6o0dO5YpU6aQnp7OokWL+Na3vnXa5z+1IAOIiIgI+i/puFCKpTdSfjvn8JFmlhWVsXRbGT+/bgzxUVbORg/qx/JtFUzOTCQv20VudipDk6Jxu9188MFuohyRfTO/Xg/s+BjWvmbdc+ygffxgOP82bOfdgi0ulW964E3jN7CU38BSfgNPOQ4s5TewQiG/nf35QS+ajq+Ct3//ft80u6amJsrLy8nMzGz3e4cOHUpSUhJ79+4NdJgivY4xhu2l9b7V7tbvq+L4ZN3Lxwxk7piBANw2NZ07Ls4g1hH0t4vQUHsQ1v/eutUeONGeOctaMnzEpRCmXImIiPQmQf/LPmHCBJxOJ4sXL+bOO+8EYMUKawWu6dOnt/u9u3fvpqKigqysrIDHKdKbrN5dyb++vZH9VUf92nMGxjM7x0X2gBPTXROi9R82vB7YtdQ6qrR9EZhjC1o4E2H8TTDxdkjW+5CIiEhvFfSiyel0cvfdd/Poo48ydOhQYmNj+eEPf8hdd91FbGwsl1xyCd/5zne44YYbeO2112hpaWHSpEmUlJTw0EMPMXbsWK644opg74ZIyCqra2RZURkDEpzMGJkCQFp/J/urjuIIt3NRVvKxZcFdDExwBjnaEFNzADa8Aev/cGK5cIChU62L0OZcCRFRwYtPREREukXQiyaAp59+mqNHjzJv3jzCwsK4+eabmT9/Pm63m61bt3Lw4EEAEhISePDBBzl48CADBw5k7ty5PPXUU37nQon0dcYYthysJb+wjKVFpWzcXwNAXrbLVzQN7h/NG/88mQlD++OMDAtmuKHH44btH8H638HOJWC8VntUAoy7CSbeBq7soIYoIiIi3Sskqg2Hw8GCBQtYsGBBq/b9+/f7Hl933XVcd9113R2eSI9gjOGx97bw8ZZSvq71X3ly3OAEJmUk+rVdlJXcneGFvspd1nlKG/4ER05aLXDYNJhwC5xzFUToSJyIiEhfFBJFk4icuUM1R9mwr5p/OLZgg81mY3tpHV/XNhIdGca0rGRm56QyMzsFV5ymkLWpqQ62vGtNwdv3+Yn2mBTrXKXzbtG5SiIiIqKiSaSn8HoNmw7UsLSwlCWFZWw9VIvNBl/8dDbJsday+vfljuCuGV6mZCYRFaFpd20yBvZ+ZhVKW94F9xGr3WaH4Xkw8VYYeRmEaQEMERERsahoEglx6/dV8ebqfSzbVkZFfbOv3WaDCUP7U1Hf5CuaNOWuHdX7YOP/WcVSVfGJ9sThcN63YdyNED8oePGJiIhIyFLRJBJiSg43EOMIJzEmEoBdZfW8vc46ty/WEc6MkSnkZruYOSqFpNjWF26WkzTWQuF7sPF/Yc/KE+2RsTD6WjjvZhgy2apARURERE5DRZNIkHm8hi/3VbHk2Gp320vr+ffLc/jni62LO8/KdnH7RenMzknlgvREIsPtQY44xHk9sHuZVSgVvg8tx69FZYOMi60V8M65CiJjghqmiIiI9BwqmkSCoNHtYUlhKfmFZSzfVkZVg9u3Lcxu41DNidXvkmMdPHbl6GCE2XMYA4c2wKa34at3oP7rE9uSR8K4G2DMPOg3JGghioiISM+lokmkm9Q2uomPshYXMAb+9a2NNLVY1wBKcEYwc9SxaXcjXSREaxGCTjm8Gzb/GTa9BZU7TrQ7E2HM9VaxNGiCpt+JiIjIN6KiSSRA3B4va/dUsbTIOqIUGW5n0Q+nA+CMDOOfLhhCVEQYedkuJg7rT3iYpt11Sn2Zterd5rdg/xcn2sOjYNQ/WEeUsmZDeGTQQhQREZHeRUWTSBeqOtLM8u1l5BeWsWJ7OXWNLb5tEWE2KuubfIs3PHH1ucEKs+dpOAxF71tT74o/AWMdocNmh4wZMHYeZF8BUfHBjVNERER6JRVNIt+AMQawLiwL8OTCrfxl/QHf9sSYSGaOSmF2TioXj0gmLkrT7jqtqQ6KPrAKpV1LwXvivC8GnWcdUTr3OogbELwYRUREpE9Q0SRyhppaPKwpPkx+YRn5RaX85tsTOTctAYC87FS2HqwlL8dFbnYq44f0I8yu82k6rakOtn8EW/4KO5dAy4kFMUg91yqSRl8LiZnBi1FERET6HBVNIp1QUd/EsqIylhaV8cn2co40e3zb8gvLfEXT3DEDuHzswGCF2TM11sL2RdZ5SjuXgKfpxLakLDj3H2H0deDKDlqIIiIi0repaBLpwIaSaq5d8CnHZuIBkBLnIC/bRW62i4uykn3tNq3S1jlHq6wjSlv/Bjvz/QulxOEw+ho45xoYMEYr34mIiEjQqWgSOabR7eGzXRXkF5YxMCGKe3NHAHDOwHhiHeEMTYwmLyeV2Tkuzh2UgF3T7s5M3dfWYg6F78OeleA9sUgGSSNOFEqpo1UoiYiISEhR0SR9WmltI0uLysgvLGXVzgoa3daqbEMTo7lnVhY2m43IcDufPpTru8aSnIHDu60iqeh9KFkDnHS4znUO5FwJ51xtfa1CSUREREKUiibps/75d2tZUljq1zYoIYrcHBd52akYc+JzvAqmTvJ64eB6KFoI2z6A8iL/7YMvsJYGz7kSkoYHJ0YRERGRM6SiSXq9huYWVm+vZNXOCh67crRvNbsBCQ5sNhg/pN+x85NSyRkYp/OSzlRLIxQvtQql7Yug/qRC1BYG6RdBzlWQfTnEDwpenCIiIiJnSUWT9EoHqo+y+KuD/F+hnX/7YjnNLda0uyvHDeKC9EQAvjczix/kjSQlzhHMUHum2oPYCj9g0q4/Ev7sXeBuOLEtMg5GzIZRl1v3zv7Bi1NERESkC6hokl5l1Y4K/t/CrRR9XXesxQ54GdzfyeycVBJjIn19B/VzBiXGHsnrgQPrYcdH1tGkrzcTDvgWV49Pg1H/AKPmQvo0CFchKiIiIr2Hiibpseoa3azcUcGQ/tGMGWxdJynGEUbR13XYbTBhaD8Gmkruvvpicgb107S7M3WkwloOfOcS2JUPDZUnbbThTZvINm86WXPvIWLweVrIQURERHotFU3So+ytPEJ+YRn5RaWsKT6M22O44YIh/MfgsQCMG9yP/7phPNNHpBAbaeODDz5ghCtWBVNneFrgwDqrSNq5GA5uwG+1O0cCZOXCyMsgazaeyAS2f/ABWbqWkoiIiPRyKpok5Lk9Xn7x0TaWFJayq/yI37bMlBiGJEb7HtvtNq4en2Z9n9vdrXH2SIeLYfcy2LUMij+Bxmr/7QPGQNYcyJoNQyZB2EmrCCq/IiIi0keoaJKQU9PgZltpHZMyrAUbIsLsLC4sZXf5EcLtNiZlJJKb7SIvJ5WM5JggR9vDHK22iqPdy2DXUqja4789qh8Mz7WKpKw8iBsQhCBFREREQouKJgk6Ywy7yo+wtKiU/MIy1u6twhFuZ/0jc4iKCAPgh7NHYrfBxSNSSHDqmkmd1twA+z63CqXiT+DQBjDeE9vt4TB4EgyfBZmzYNB5EKa3BREREZGT6dORBM3Gkmr+tuEg+UWl7K1s8Ns2uL+TQzWNviNJV43T9X06paXJWuWueIVVJJWsAe8p0+iSR1oF0vBZ1kp3jrjgxCoiIiLSQ6hokm5TWd+EMzKM6Ehr2K3aWcGrnxYDEBlmZ3JmIrNzUsnNdvmdpyTtcDfCgbWw51PYu8oqkloa/fvEp0HGDMiYbt0S0oITq4iIiEgPpaJJAsYYw7bSOvILy1haVMb6fVX8+p/G+xZquHR0KnsqjpCXk8q0EcnEOjQcO9RUbxVJez+zCqX9X4Cnyb9PdBKkXwyZM6xiKTFTq9uJiIiIfAP6lCpdqrnFy2e7KlhaVEZ+YRkHqo/6bd96qNZXNGW54pj/rXHBCLPnqCuFkgLYV2Cdm3RoExiPf58YlzXNLv0iGDYNUkapSBIRERHpQiqa5Btze7xEhNkBqGpo5rbXvvBtc4TbmTo8ibycVPJyXAxMcAYrzNDn9UDZVmuK3f4voGQ1HN7dul/CUBg6GYZdZBVLSVkqkkREREQCSEWTnDFjDFsO1h6bdldKQnQkv//OJABS46OYneMiJS6KvGwXF2Ul44wMC3LEIepIpTXVrmQN7F9jLeDQXH9KJxukjoahU2DohdZ9wuCghCsiIiLSV6lokk452uzhs10VLCksY1lRGV/XnlhsIDLcztFmj684euXWC4IVZuhqboBDG+HAOji43ro/9RpJAJFxMHiitQz4kEkw+AJw9uvuaEVERETkJCqapFPu+dN6lhaV+R5HR4YxLSuZvBwXs7JdOpp0MncjlG6BQ18eK5S+tKbdnXouEkDSiBPF0ZBJkJINduVSREREJJSoaBIfr9ewcX+1bxGH126/gNT4KACmj0hm29d15OW4yMtJZXJGou/Cs31a8xEoK4SDX1oXjj24EcoLwdvSum9sKqSdD2kTIG2idSFZHUUSERERCXkqmvq4+qYWVu0oJ7+wjGXbyqiob/ZtW1pUxo2ThgLw7SnDuHVqOra+uuCAMVBfCl9vhq83wddfWV9X7gRM6/7RSTBwPAwcZxVHaRMhfpAWbBARERHpgVQ09WGf7qzg9te+oNnj9bXFOcKZPjLFmnY3yuVrP746Xp/QVA/lRdYUu7Kt1q10KzRUtN0/NhUGjIVB460iaeB4a7EGFUgiIiIivYKKpj6gxePly5Jq8gvLGJ4Sw7fOHwLA6EHxtHi9DEuKJi/bWhL8gvREIsP7SIHUVA8V26F8G1Rss+5Lt0D13rb72+zWOUgDxvjfYl1t9xcRERGRXkFFUy9Vc9TNJ9vLWVpkTburbnADcP6w/r6iqV90JCt/nMughKjeO+3OGKg9BLV7oGKHNZ2ufJtVLNWUnP77YlPBdY51Sz12n5INkdHdFrqIiIiIhAYVTb2MMYY7f7+W5dvKafGeONcmwRnBzFEpzM5J9euf1q8XXGzWGDhSAVXF1sVgDxdD5Q7Cy7dzefl2wjc0nf57Y1yQMsq6JY8CVza4RkNMUvfFLyIiIiIhTUVTD+b2eFm7p4r1+6q4Z1YWADabDbvNRovXkOWKJS/bRW62i4nD+hPek89LammC6hJr6lz1Xqjae1KRtAea61p9iw1rgBtbGLb+w6ypdUlZkDLSOmqUPBKiE7t7T0RERESkh1HR1MNUHWlmxfZylhSWsmJ7OXWN1tLWl48ZSHpyDAAPXjqKn16ew7CkmGCG2nnGQGM11ByAmv1Qu//E19V7oXof1B3q4ElsEJ8GiRnQPx2SR9CSkM6KLQeZfvUtRET1kFyIiIiISMgJiaLJGMMTTzzBSy+9RE1NDZdeeikvv/wyycnJrfp+8skn3H///WzZsoXhw4fz7LPPcumllwYh6u61fFsZ/71sJ+v2VnHSrDsSYyKZNcqF15xoHJkaF4QIT6Ol2Vqqu+5rq/Dx3R+71R60CiT3kY6fKyIa+g2DfkOtW2KmVSQlZlrtEVF+3Y3bTf2uDyAsMkA7JyIiIiJ9QUgUTfPnz+e5557j9ddfJykpiTvuuINbb72VhQsX+vUrLi5m7ty53HPPPbz++uv85je/4dprr6WwsJBhw4YFKfqu19TiYU3xYYYmRvuOFjW3ePliTxUA2QPiyM22LjI7fkg/wuzduIiD1wONNdBQ6X+rL4Mj5Sfdl1pfN1Z3/rmjk6yjRQmDj92nWcVQ/2HWfXSSlvEWERERkW4X9KLJ6/Uyf/58HnnkEa688koAnn32WebOnUtxcTEZGRm+vs8//zxZWVk888wzADz33HO89957vPrqqzz++ONBib+rVNQ3sbSojKWFZazcUc6RZg/35Wbxr5eMAmDaiGSeuHo0udkuBvf/Biu4eT3QXA9NdSfdaq3lt5tqrYLoaLVV7LS6r7JuxtveT2jNHgFxAyBuoP99/KBj94Otr7UynYiIiIiEoKAXTZs3b6aiooLLLrvM1zZz5kzsdjsFBQV+RdOyZcv8+oWHhzN9+nQKCgq6Neau0lz4IaW71vLsc1spOdyAzXiJBGbjJSEmjHEV22FdAXhbiPa2cItxw5YW8LrB0wItjeBptu5bjt83WosmuI9aU96aG8DdAM1HrPuWxq4JPirBOvLjuyVDbIq1Gl2sC2JSrGW7Y10Q1Q/sPXgRChERERHp04JeNO3evRvArzhyOp2kpKRw4MCBVn1P7gcwdOhQNm3adNrnb2pqoqnpxJLTtbW1ALjdbtxu9zeO/5twfvgDvnv0sPUg4pSNHmD7sVsAGHs4OOLBEQeRcRhHLETGQlQCJqqfVeg4T/o6KgHjTLRWm3MmQtipAbfD47Fu3ez47zfYv+feSvkNLOU3sJTfwFJ+A085DizlN7BCKb+djSHoRVN9fT12ux2Hw+HXHh0dTWNjY6u+0dHRHfY72c9//vM2p+59/PHHrZ6ru02OGMqRlmRsNhvR4bZj5ybZMLZj99gwtjC8trCT7u0YWzheWxheWwQeewReW/iJr+2ReG3htNgdeOwOPPZI39e++7AovLaI058f5AUajt18ao7digOblABYvHhxsEPo1ZTfwFJ+A0v5DSzlN/CU48BSfgMrFPLb0NDQcSdCoGhyOBx4vV5aWloIDz8RTmNjY6uixuFw0Nzc7NfWVr+TPfzwwzzwwAO+x7W1tQwZMoRLLrmE+Pj4LtqLs+N2z2H14sXMmTOHiIgzOHIjneJ2u1ms/AaM8htYym9gKb+BpfwGnnIcWMpvYIVSfo/PQutI0IumtLQ0APbv3096ejpgTakrLy8nMzOzVd+SkhK/tpKSklb9TuZwOFodxQKIiIgI+i/puFCKpTdSfgNL+Q0s5TewlN/AUn4DTzkOLOU3sEIhv539+UE/O3/ChAk4nU6/w3MrVqwAYPr06X59p02b5tfP4/GwfPly8vLyuidYERERERHpc4JeNDmdTu6++24effRRPvroIz799FN++MMfctdddxEbG8sll1zC//7v/wLw/e9/nzVr1vDEE0/w1Vdfcd999+H1erntttuCuxMiIiIiItJrBX16HsDTTz/N0aNHmTdvHmFhYdx8883Mnz8ft9vN1q1bOXjwIADnnXceb775Jg899BBPP/00kyZN4uOPPyYuLi7IeyAiIiIiIr1VSBRNDoeDBQsWsGDBglbt+/fv92u7/vrruf7667szPBERERER6cOCPj1PREREREQklKloEhERERERaYeKJhERERERkXaoaBIREREREWmHiiYREREREZF2qGgSERERERFph4omERERERGRdqhoEhERERERaYeKJhERERERkXaoaBIREREREWmHiiYREREREZF2qGgSERERERFph4omERERERGRdoQHO4DuZowBoLa2NsiRgNvtpqGhgdraWiIiIoIdTq+j/AaW8htYym9gKb+BpfwGnnIcWMpvYIVSfo/XBMdrhNPpc0VTXV0dAEOGDAlyJCIiIiIiEgrq6upISEg47Xab6ais6mW8Xi8HDx4kLi4Om80W1Fhqa2sZMmQIJSUlxMfHBzWW3kj5DSzlN7CU38BSfgNL+Q085TiwlN/ACqX8GmOoq6tj0KBB2O2nP3Opzx1pstvtDB48ONhh+ImPjw/6gOnNlN/AUn4DS/kNLOU3sJTfwFOOA0v5DaxQyW97R5iO00IQIiIiIiIi7VDRJCIiIiIi0g4VTUHkcDh47LHHcDgcwQ6lV1J+A0v5DSzlN7CU38BSfgNPOQ4s5TewemJ++9xCECIiIiIiImdCR5pERERERETaoaJJRERERESkHSqaRERERERE2qGiSUREREREpB0qmrqYMYbHH3+cQYMGERMTw3XXXUdFRUWbfT/55BMmTpxIVFQUo0eP5qOPPvLb/tVXXzF9+nScTieZmZn88Y9/7I5dCGmdze/Ro0e5//77GTBgALGxsUydOpUVK1b49Rk2bBg2m83vdrrfVV/R2fx6PB7sdrtf7mJjY/36aPy21tn8pqentxqbNpuNvLw8Xx+N39PbvHkzEydOZNWqVaft09H4LCkp4YorriAmJoZBgwbxi1/8ItBh9xgd5dfj8fDkk08ybNgwoqOjGT9+PH/5y1/8+syYMaPV+F27dm13hB/yOjN+O3r9a/yeXkf5nTlzZpvvv8OHD/f10fht28aNG7nkkkuIjo5mwIAB3H777VRWVrbZt0d+BjbSpZ555hmTmJho3nvvPfPpp5+a7OxsM3fu3Fb9du/ebWJiYsyPfvQjs2nTJnP33Xcbp9Np9uzZY4wxprq62gwYMMDccsstZuPGjebJJ580drvdfP755929SyGls/l99tlnzTXXXGOWLVtm1q5da2688UYTExNjiouLfX1iYmLMG2+8YXbs2OG7eTyebtyb0NPZ/JaXlxvALF++3Je7Xbt2+bZr/Lats/nds2eP37gsLCw0LpfLvPTSS74+Gr+trVu3zsybN884nU4DmJUrV7bZr6Px2dLSYsaMGWMuu+wys27dOvPyyy8bu91u3nrrre7cnZDT2fz+5S9/MdOnTzcffvih+fLLL83999/f6vU/evRo88wzz/iN38bGxu7alZDU2fwa0/7rX+O3bZ3N7/79+/3yumPHDjNmzBjz8MMP+/po/LbtwgsvNE899ZTZuHGjef/9901GRkav+gysoqkLeTwek5ycbH71q1/52j744AMDmN27d/v1vf/++824ceN8j91ut0lLSzOPPvqoMcaY//qv/zIul8s0NTX5+kyePNnccsstAd2HUHYm+d27d6/f4+bmZhMdHW1efPFFY4wxTU1NBjCbNm0KeNw9xZnkd9u2bQYwtbW1bT6Xxm9rZ5LfU73yyitm2LBhprm52Rij8Xs6P/3pT83NN99s8vPz2/1Q1NH4/Nvf/mYiIiJMaWmpb/u8efPM9OnTA7sDIa6z+T1w4IBpaWnxaxsxYoR56KGHfI8HDhxo3nvvvYDG29N0Nr8dvf41ftvW2fyeasmSJSYuLs5UVFT42jR+23bqZ6833njD2O12c+TIEb/2nvoZOLzbD231Yps3b6aiooLLLrvM1zZz5kzsdjsFBQVkZGT42pctW+bXLzw8nOnTp1NQUODbPmvWLCIjI319cnNzeeedd7phT0LTmeR36NChft8bHh5OeHg4Ho8HgMOHDwOQnJzcDZH3DGeS38OHDxMZGUlcXFybz6Xx29qZ5Pdkbrebp556iocffpiIiAhA4/d0nnzySWw2G3v27Gm3X0fjc9myZUyYMAGXy+XbnpeXxw9+8AOMMdhstoDEH+o6m99Bgwa1aouKivK9/4I1hjV+/XU2vx29/jV+29bZ/J7qscce45577iEpKcnXpvHbtlM/e0VFReH1elv166mfgXVOUxfavXs3gN+HH6fTSUpKCgcOHGjV99QPSUOHDvX162h7X3Qm+T3VW2+9RW1tLbNmzQLwzbHNyMggLS2Nq666ik2bNgUo8p7hTPJbWVlJc3MzTqeTYcOGcdNNN/n9IdL4be1sx++f//xnqqurueWWW3xtGr9t6+yHwbN9/21sbDzt/Py+4Gw/bBcUFLB582Zyc3MBOHLkCE1NTcycOROXy0VeXh4rV67sylB7pM7mt6PXv8Zv285m/H7++ecUFBRw7733+to0fjvHGMP//M//MHnyZKKjo/229dTPwCqaulB9fT12ux2Hw+HXHh0dTWNjY6u+pw6ik/t1tL0vOpP8nuz999/njjvu4N/+7d/IyckBrBdfQUEBX3zxBS+++CKVlZXMmDGD/fv3B3QfQtmZ5Hfy5MmsWbOG1atXM3/+fDZu3MisWbOoq6vzPZfGr7+zHb8vvPACt912G06n09em8fvNnO37L9Cnx/DZWL16NVdffTXz5s3z/Wc5MjKSzz//nLVr1/LGG28QHR1NXl4eX375ZZCj7Rk6ev1r/HadF154gauuuoq0tDRfm8Zvx9xuN9/97ndZtmwZL7zwQqvtPfUzsIqmLuRwOPB6vbS0tPi1NzY2tvrlOxwOmpubT9uvo+190ZnkF8Dr9fLoo49yzTXX8OMf/5j//M//9G2Li4tj8uTJjBkzhiuvvJIPP/wQgDfffDOwOxHCziS/ycnJXHDBBYwdO5Z58+bx4YcfsnfvXhYtWuR7Lo1ff2c6fgE2bdrEZ599xp133unXrvH7zZzt+y/Qp8fwmfrNb37DjBkzuPbaa/1WvoqIiGDKlCmMGTOGOXPm8Ne//pWMjAxeeeWVIEbbc3T0+tf47RoVFRX8+c9/bvX+q/Hbvv379zNz5kwWLlzI8uXLOf/881v16amfgVU0daHj/4k4+b+9TU1NlJeXk5mZ2apvSUmJX1tJSYmvX0fb+6Izya/X6+XGG2/k5ZdfZtGiRTzyyCPtPnd8fDxZWVns3bu36wPvIc4kv6caOnQoSUlJvvxp/LZ2Nvl9++23yc7O9h0hPR2N3zNztu+/CQkJJCYmdlucPdmDDz7Ij370I1577TVefPFF3/l4bQkPD2fs2LEav2fp1Ne/xm/X+Nvf/kZUVJTfpR7aovF7wvbt25k8eTLx8fFs3LiRSZMmtdmvp34GVtHUhSZMmIDT6WTx4sW+tuPXBpo+fbpf32nTpvn183g8LF++3PfinDZtGkuXLvU7cTY/P7/DF29vdib5XbBgAcuXL2f16tXMnj27w+eurq5m+/btZGVldW3QPciZ5PdUu3fvpqKiwpc/jd/Wzia/7777Ltdcc02Hz63xe2Y6Gp/Tpk1jzZo11NTUtLld2vf++++zYMECVqxYwY033thhf7fbzZdffqnxe5ZOff1r/HaNd999l7lz5/otRtAWjd8TbrrpJmbMmMHChQtJSUk5bb8e+xk4qGv39UIPPPCAGTBggFm0aJFZtWqVycnJMffee69pamoyc+bMMW+++aYxxpj169eb8PBw8/jjj5vNmzebu+++2wwaNMi3hPOBAwdMXFycueuuu8zmzZvNE088YWJjY31r2PdVnc3v1KlTzQ033NDqWgslJSXGGGPef/9988tf/tKsW7fOLFmyxEybNs2kpaWZw4cPB3P3gq6z+X311VfNyy+/bDZs2GD+/ve/m9GjR5uxY8cat9ttjNH4PZ3O5tcYYyorKw1gPvjgg1bPo/HbvuLi4lZLCt9www3ml7/8pTGm4/F55MgRM3jwYHPttdeaDRs2mJdeeslERkaagoKCoOxPqOkovzfddJO5+OKLW73/Hl9a/4svvjCPPfaYWb16tVm5cqW55pprTFxcnNm5c2dQ9ifUdJTfjl7/Gr/t6yi/xhjj9XpNfHy8WbBgQavv1/ht2/bt2w1g3n777Vav/erq6l7xGVhFUxdrbGw0d999t4mPjzf9+/c39913n2lsbDT19fUmLS3N70X59ttvm+HDhxuHw2Euvvhi89VXX/k91/Lly825555rIiMjzXnnnWc++eST7t6dkNPZ/GZkZBig1W3ixInGGGNWrVplsrOzTVRUlElLSzPf/va3zYEDB4K5ayGhs/l95513TEZGhnE4HCY9Pd1873vfM1VVVX7PpfHb2pm8PyxZssQA5tChQ62eR+O3fW19KBo3bpz5/ve/73vc0fjcvHmzmTJliomMjDSjRo0y77zzTrfFH+o6yu+sWbPafP9NSkoyxljXeRs/fryJjo42KSkp5qqrrjJFRUVB2ZdQ1FF+O/P61/g9vc68P+zcudMAbV5MVeO3bStWrGjzdQ+YX//6173iM7DNGGO655iWiIiIiIhIz6NzmkRERERERNqhoklERERERKQdKppERERERETaoaJJRERERESkHSqaRERERERE2qGiSUREREREpB0qmkRERERERNqhoklERERERKQdKppERERERETaoaJJRERERESkHSqaRERERERE2qGiSUREREREpB0qmkRERERERNqhoklERPqMN998E6fTyaFDh3xtt99+O2PHjqWmpiaIkYmISCizGWNMsIMQERHpDsYYxo8fz/Tp03n++ed57LHHePXVVykoKCAtLS3Y4YmISIgKD3YAIiIi3cVms/HUU09x/fXXM2DAAJ5//nlWrlypgklERNqlI00iItLnTJgwgS1btvDxxx8zY8aMYIcjIiIhTuc0iYhIn7Jo0SKKiorweDykpqYGOxwREekBdKRJRET6jPXr1zNz5kxeeuklXn/9deLj43n77beDHZaIiIQ4ndMkIiJ9wp49e7j88sv5yU9+wo033khmZiYXXngh69evZ8KECcEOT0REQpiONImISK93+PBhpk6dysyZM3nxxRd97Zdffjkej4dFixYFMToREQl1KppERERERETaoYUgRERERERE2qGiSUREREREpB0qmkRERERERNqhoklERERERKQdKppERERERETaoaJJRERERESkHSqaRERERERE2qGiSUREREREpB0qmkRERERERNqhoklERERERKQdKppERERERETaoaJJRERERESkHf8fqfT5sky55nYAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "数值导数和理论导数之间的最大差异：1.9999499999960832\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import quad\n",
    "\n",
    "# 定义函数 f(x, y)\n",
    "def f(x, y):\n",
    "    # 例如 f(x, y) = x * y^2，选择一个简单的连续函数\n",
    "    return x * y**2\n",
    "\n",
    "# 定义函数 f_x(x, y) 的偏导数\n",
    "def f_x(x, y):\n",
    "    # 偏导数 f_x(x, y) = y^2\n",
    "    return y**2\n",
    "\n",
    "# 计算 φ(x) = ∫[c,d] f(x, y) dy\n",
    "def phi(x, c, d):\n",
    "    result, _ = quad(f, c, d, args=(x,))\n",
    "    return result\n",
    "\n",
    "# 计算 φ'(x) 的数值近似\n",
    "def derivative_phi(x, c, d, delta_x=1e-4):\n",
    "    # 使用数值方法计算 φ'(x) ≈ (φ(x + Δx) - φ(x)) / Δx\n",
    "    return (phi(x + delta_x, c, d) - phi(x, c, d)) / delta_x\n",
    "\n",
    "# 计算 φ'(x) 的理论值\n",
    "def theoretical_derivative(x, c, d):\n",
    "    # 根据定理3，理论上 φ'(x) = ∫[c,d] f_x(x, y) dy\n",
    "    result, _ = quad(f_x, c, d, args=(x,))\n",
    "    return result\n",
    "\n",
    "# 比较数值导数和理论导数\n",
    "def compare_derivatives(a, b, c, d):\n",
    "    x_vals = np.linspace(a, b, 100)\n",
    "    numeric_derivatives = np.array([derivative_phi(x, c, d) for x in x_vals])\n",
    "    theoretical_derivatives = np.array([theoretical_derivative(x, c, d) for x in x_vals])\n",
    "\n",
    "    # 绘制数值导数和理论导数的比较图\n",
    "    plt.figure(figsize=(10, 6))\n",
    "    plt.plot(x_vals, numeric_derivatives, label=r'数值导数 $\\varphi\\'(x)$', linestyle='dashed')\n",
    "    plt.plot(x_vals, theoretical_derivatives, label=r'理论导数 $\\int_{c}^{d} f_{x}(x, y) dy$', linestyle='solid')\n",
    "    plt.title(r'数值导数与理论导数的比较')\n",
    "    plt.xlabel(r'$x$')\n",
    "    plt.ylabel(r'导数值')\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "    plt.show()\n",
    "\n",
    "    # 计算数值导数和理论导数的差异\n",
    "    max_diff = np.max(np.abs(numeric_derivatives - theoretical_derivatives))\n",
    "    return max_diff\n",
    "\n",
    "# 设置积分区间 [a, b] 和 [c, d]\n",
    "a, b = 0, 2  # 对 x 的区间 [a, b]\n",
    "c, d = 0, 1  # 对 y 的区间 [c, d]\n",
    "\n",
    "# 比较数值导数和理论导数\n",
    "max_diff = compare_derivatives(a, b, c, d)\n",
    "\n",
    "print(f\"数值导数和理论导数之间的最大差异：{max_diff}\")\n"
   ]
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